o
    eA                    @   s\  d dl Z d dlmZ d dlmZ d dlmZ d dlmZ d dl	m
Z
 d dlmZmZ d dlmZ d d	lmZ d d
lmZ d dlmZ d dlmZ d dlmZmZmZ d dlmZmZ d dlm Z  d dl!m"Z" d dl#m$Z$ d dl%m&Z&m'Z' d dl(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3 e/Z4e2Z5G dd deZ6ee6dd Z7dd Z8e8Z9dd Z:dS )    N)S)Add)Tuple)FunctionMul)NumberRational)Pow)default_sort_keySymbol)SympifyError)requires_partial)
PRECEDENCE
precedenceprecedence_traditional)Printerprint_function)sstr)has_variety)sympy_deprecation_warning)
prettyForm
stringPict)hobjvobjxobjxsympretty_symbolpretty_atompretty_use_unicodegreek_unicodeUpretty_try_use_unicode	annotatedc                   @   s	  e Zd ZdZdZddddddddddd
Zdd	d
Zdd Zedd Z	dd Z
dd Zdd Zdd ZdddZeZdd Zdd Zdd Zd d! Zd"d# Zd$d% Zd&d' Zd(d) Zd*d+ ZeZeZeZeZeZeZeZeZ eZ!d,d- Z"d.d/ Z#d0d1 Z$d2d3 Z%d4d5 Z&d6d7 Z'd8d9 Z(dd:d;Z)d<d= Z*d>d? Z+d@dA Z,dBdC Z-dDdE Z.ddFdGZ/ddHdIZ0dJdK Z1dLdM Z2dNdO Z3dPdQ Z4dRdS Z5dTdU Z6dVdW Z7dXdY Z8dZd[ Z9d\d] Z:d^d_ Z;d`da Z<dbdc Z=ddfdgZ>dhdi Z?djdk Z@dldm ZAdndo ZBdpdq ZCdrds ZDdtdu ZEdvdw ZFdxdy ZGdzd{ ZHd|d} ZId~d ZJdd ZKdd ZLdd ZMdd ZNdd ZOdd ZPdd ZQdd ZRdd ZSdd ZTdd ZUdd ZVdd ZWdd ZXdd ZYdd ZZdd Z[dd Z\i fddZ]dd Z^dd Z_dd Z`dd Zadd Zbdd Zcdd Zddd Zedd ZfdddZgdd Zhdd Zidd Zjdd Zk		ĐdddƄZlddȄ Zmddʄ Zndd̄ Zodd΄ Zp			ĐdddфZqddӄ ZreddՄ Zsddׄ Ztddل Zuddۄ Zvdd݄ Zwdd߄ Zxdd Zydd Zzdd Z{dd Z|dd Z}dd Z~dd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zd d Zdd Zdd Zdd Zdd	 Zd
d Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd ZdܐddZd d! Zd"d# Zd$d% Zd&d' Zd(d) Zd*d+ Zd,d- Zd.d/ Zd0d1 Zd2d3 Zd4d5 Zd6d7 Zd8d9 Zd:d; Zd<d= Zd>d? Zd@dA ZdBdC ZdDdE ZdFdG ZdHdI ZdJdK ZdLdM ZdNdO ZeZeZeZdddϐdPdQ dfdRdSZdTdU ZdVdW ZdXdY ZdZd[ Zd\d] Zd^d_ Zd`da Zdbdc Zddde Zdfdg Zdhdi Zdjdk Zdldm Zdndo Zdpdq ZÐdrds ZĐdtdu ZŐdvdw ZƐdxdy Zǐdzd{ ZȐd|d} Zɐd~d Zʐdd Zːdd Z̐dd Z͐dd Zΐdd Zϐdd ZАdd Zѐdd ZҐdd ZeZԐdd ZՐdd Z֐dd Zאdd Zؐdd Zِdd Zڐdd Zېdd Zܐdd Zݐdd Zސdd Zߐdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd ZddÄ ZdĐdń ZdƐdǄ ZdȐdɄ Zdʐd˄ Zd̐d̈́ Zdΐdτ ZdАdф ZdҐdӄ ZdԐdՄ Zd֐dׄ Zdؐdل Zdڐdۄ ZdS (  PrettyPrinterz?Printer, which converts an expression into 2D ASCII-art figure.Z_prettyNautoTplaini)
order	full_precuse_unicodeZ	wrap_linenum_columnsuse_unicode_sqrt_charroot_notationmat_symbol_styleimaginary_unitperm_cyclicc                 C   sV   t | | t| jd tstd| jd | jd dvr)td| jd d S )Nr0   z&'imaginary_unit' must a string, not {})r(   jz4'imaginary_unit' must be either 'i' or 'j', not '{}')r   __init__
isinstance	_settingsstr	TypeErrorformat
ValueError)selfsettings r<   LD:\Projects\ConvertPro\env\Lib\site-packages\sympy/printing/pretty/pretty.pyr3   /   s   zPrettyPrinter.__init__c                 C      t t|S Nr   r6   r:   exprr<   r<   r=   emptyPrinter7      zPrettyPrinter.emptyPrinterc                 C   s   | j d rdS t S )Nr+   T)r5   r    r:   r<   r<   r=   _use_unicode:   s   
zPrettyPrinter._use_unicodec                 C   s   |  |jdi | jS )Nr<   )_printrenderr5   rA   r<   r<   r=   doprintA      zPrettyPrinter.doprintc                 C   s   |S r?   r<   r:   er<   r<   r=   _print_stringPictE   s   zPrettyPrinter._print_stringPictc                 C   s   t |S r?   )r   rK   r<   r<   r=   _print_basestringH   s   zPrettyPrinter._print_basestringc                 C   s&   t | |j  }t |d }|S )Natan2)r   
_print_seqargsparensleftr:   rL   pformr<   r<   r=   _print_atan2K   s   zPrettyPrinter._print_atan2Fc                 C   s   t |j|}t|S r?   )r   namer   )r:   rL   Z	bold_nameZsymbr<   r<   r=   _print_SymbolP   s   zPrettyPrinter._print_Symbolc                 C   s   |  || jd dkS )Nr/   bold)rX   r5   rK   r<   r<   r=   _print_MatrixSymbolT   s   z!PrettyPrinter._print_MatrixSymbolc                 C   s,   | j d }|dkr| jdk}tt||dS )Nr*   r&      )r*   )r5   Z_print_levelr   r   )r:   rL   r*   r<   r<   r=   _print_FloatW   s   

zPrettyPrinter._print_Floatc                 C   ~   |j }|j}| |}t|d }t|d }t|| td }t|d }t|| | }t|d }|S )N()MULTIPLICATION SIGNZ_expr1Z_expr2rG   r   rS   rightr"   r:   rL   Zvec1Zvec2rU   r<   r<   r=   _print_Cross_      
zPrettyPrinter._print_Crossc                 C   `   |j }| |}t|d }t|d }t|| td }t|| td }|S )Nr^   r_   r`   NABLAZ_exprrG   r   rS   rb   r"   r:   rL   ZvecrU   r<   r<   r=   _print_Curlk      
zPrettyPrinter._print_Curlc                 C   rf   )Nr^   r_   DOT OPERATORrg   rh   ri   r<   r<   r=   _print_Divergencet   rk   zPrettyPrinter._print_Divergencec                 C   r]   )Nr^   r_   rl   ra   rc   r<   r<   r=   
_print_Dot}   re   zPrettyPrinter._print_Dotc                 C   H   |j }| |}t|d }t|d }t|| td }|S )Nr^   r_   rg   rh   r:   rL   funcrU   r<   r<   r=   _print_Gradient      
zPrettyPrinter._print_Gradientc                 C   ro   )Nr^   r_   Z	INCREMENTrh   rp   r<   r<   r=   _print_Laplacian   rs   zPrettyPrinter._print_Laplacianc                 C   s4   zt t|jj| dW S  ty   | | Y S w )N)printer)r   r   	__class____name__KeyErrorrC   rK   r<   r<   r=   _print_Atom   s
   zPrettyPrinter._print_Atomc                 C   s&   | j r| |S ddg}| |ddS )Nz-ooZoor^   r_   )rF   ry   rP   )r:   rL   Zinf_listr<   r<   r=   _print_Reals   s   
zPrettyPrinter._print_Realsc                 C   D   |j d }| |}|jr|js|jst|  }t|d }|S Nr   !)rQ   rG   
is_Integeris_nonnegative	is_Symbolr   rR   rS   r:   rL   xrU   r<   r<   r=   _print_subfactorial      

z!PrettyPrinter._print_subfactorialc                 C   r{   r|   rQ   rG   r~   r   r   r   rR   rb   r   r<   r<   r=   _print_factorial   r   zPrettyPrinter._print_factorialc                 C   r{   )Nr   z!!r   r   r<   r<   r=   _print_factorial2   r   zPrettyPrinter._print_factorial2c                 C   st   |j \}}| |}| |}dt| |  }t|| }t|| }t|dd }|jd d |_|S )N r^   r_   r[      )rQ   rG   maxwidthr   aboverR   baseline)r:   rL   nkZn_pformZk_pformbarrU   r<   r<   r=   _print_binomial   s   


zPrettyPrinter._print_binomialc                 C   sL   t dt|j d }| |j}| |j}t t|||dt ji}|S )Nr   binding)	r   r   Zrel_oprG   lhsrhsr   nextOPENr:   rL   oplrrU   r<   r<   r=   _print_Relational   s
   zPrettyPrinter._print_Relationalc                 C   s   ddl m}m} | jr@|jd }| |}t||r!| j|ddS t||r-| j|ddS |j	r9|j
s9t|  }t|d S | |S )Nr   )
EquivalentImpliesu   ⇎)altcharu   ↛   ¬)Zsympy.logic.boolalgr   r   rF   rQ   rG   r4   _print_Equivalent_print_Implies
is_Booleanis_Notr   rR   rS   _print_Function)r:   rL   r   r   argrU   r<   r<   r=   
_print_Not   s   




zPrettyPrinter._print_Notc                 C   s   |j }|rt|j td}|d }| |}|jr!|js!t|  }|dd  D ]#}| |}|jr:|js:t|  }t|d|  }t|| }q'|S )Nkeyr   r[    %s )	rQ   sortedr   rG   r   r   r   rR   rb   )r:   rL   charsortrQ   r   rU   	pform_argr<   r<   r=   Z__print_Boolean   s   

zPrettyPrinter.__print_Booleanc                 C       | j r	| |dS | j|ddS )N   ∧Tr   rF   _PrettyPrinter__print_Booleanr   rK   r<   r<   r=   
_print_And     zPrettyPrinter._print_Andc                 C   r   )Nu   ∨Tr   r   rK   r<   r<   r=   	_print_Or  r   zPrettyPrinter._print_Orc                 C   r   )Nu   ⊻Tr   r   rK   r<   r<   r=   
_print_Xor  r   zPrettyPrinter._print_Xorc                 C   r   )Nu   ⊼Tr   r   rK   r<   r<   r=   _print_Nand  r   zPrettyPrinter._print_Nandc                 C   r   )Nu   ⊽Tr   r   rK   r<   r<   r=   
_print_Nor$  r   zPrettyPrinter._print_Norc                 C   s$   | j r| j||p	dddS | |S )Nu   →Fr   r   r:   rL   r   r<   r<   r=   r   *  s   
zPrettyPrinter._print_Impliesc                 C   s$   | j r| ||p	dS | j|ddS )Nu   ⇔Tr   r   r   r<   r<   r=   r   0  s   zPrettyPrinter._print_Equivalentc                 C   s(   |  |jd }t|td|  S )Nr   _)rG   rQ   r   r   r   r   rT   r<   r<   r=   _print_conjugate6  s   zPrettyPrinter._print_conjugatec                 C   s$   |  |jd }t|dd }|S )Nr   |)rG   rQ   r   rR   rT   r<   r<   r=   
_print_Abs:  s   zPrettyPrinter._print_Absc                 C   4   | j r| |jd }t|dd }|S | |S )Nr   lfloorrfloorrF   rG   rQ   r   rR   r   rT   r<   r<   r=   _print_floor?  
   
zPrettyPrinter._print_floorc                 C   r   )Nr   lceilrceilr   rT   r<   r<   r=   _print_ceilingG  r   zPrettyPrinter._print_ceilingc                 C   s  t |jr| jrtd}nd}d }d}t|jD ]8\}}| |}t|| }||7 }|j	r3|dkr;|tt
| }|d u rB|}qt|d }t|| }qt| |j dtji}	t|}
|dkdkrq|
tt
| }
t|
tj| }
|
jd |
_tt|
|	 }
tj|
_|
S )NPARTIAL DIFFERENTIALdr   r[   r   r   F)r   rB   rF   r"   reversedZvariable_countrG   r   rS   r~   r6   rb   rR   FUNCbelowr   LINEr   r   MULr   )r:   derivderiv_symbolr   Zcount_total_derivsymnumsdsfrU   r<   r<   r=   _print_DerivativeO  s8   

zPrettyPrinter._print_Derivativec                 C   s   ddl m}m} || krtd}t|  S || j}|g kr0| |j	d }t|  S td}|D ]}| t
t|dd}t|| }q6|S )Nr   PermutationCycle r[   ,) sympy.combinatorics.permutationsr   r   r   r   rR   listZcyclic_formrG   sizer6   tuplereplacerb   )r:   Zdcr   r   ZcycZdc_listr(   r   r<   r<   r=   _print_Cyclet  s   
zPrettyPrinter._print_Cyclec                 C   s   ddl m}m} |j}|d urtd| ddddd n| jd	d
}|r,| ||S |j}t	t
t|}td}d
}t||D ](\}	}
| |	}| |
}t|| }|r\d}nt|d }t|| }qBt|  S )Nr   r   zw
                Setting Permutation.print_cyclic is deprecated. Instead use
                init_printing(perm_cyclic=z).
                z1.6z#deprecated-permutation-print_cyclic   )Zdeprecated_since_versionZactive_deprecations_target
stacklevelr1   Tr   Fr   )r   r   r   Zprint_cyclicr   r5   getr   Z
array_formr   rangelenr   ziprG   r   r   rS   rb   rR   )r:   rB   r   r   r1   lowerupperresultfirstur   s1s2colr<   r<   r=   _print_Permutation  s6   


z PrettyPrinter._print_Permutationc                 C   s  |j }| |}|jrt|  }|}|jD ]}| |d }| dkr+t|  }t|d| }qd}d }|jD ]}	| }
|
d }| j	 }|rO|d7 }t
d|}t|}|j||
 d  |_t|	dkrt|	dkrytd}| |	d }t|	dkr| |	d }| |	d }|rtdd|  }t|d	|  }tdd
|  }t|d	|  }t|| }t|| }|st|d	 }|r|}d}q;t|| }q;t|| }tj|_|S )Nr   r[   z dTr   intr      r      F)functionrG   is_Addr   rR   limitsr   rb   heightrF   r   r   r   r   rS   r   r   r   r   )r:   Zintegralr   prettyFr   r   Z	prettyArgZ	firsttermr   limhH
ascii_modeZvintrU   ZprettyAZprettyBZspcr<   r<   r=   _print_Integral  s\   



zPrettyPrinter._print_Integralc                 C   s  |j }| |}tdd}tdd}tdd}| jr!tdd}d}| }d}d}	d}
|jD ]}| |\}}|d d	 d
 d }|| ||d   | | g}t|d D ]}|d| d|d   | d  qVt	d}t
|j|  }t|	| }	|r| }
t
|| }t
|| }|rd|_d}| }t	d}t
|jdg|d    }t
|| }t
|| }q.|	|
d  |_t
j|_|S )Nr   r[   r   -u   ┬Tr   r      r   r   r   F)termrG   r   rF   r   r   '_PrettyPrinter__print_SumProduct_Limitsr   appendr   r   stackr   r   r   r   rb   r   r   )r:   rB   rq   Zpretty_funcZhorizontal_chrZ
corner_chrZvertical_chrZfunc_heightr   	max_uppersign_heightr   Zpretty_lowerZpretty_upperr   Z
sign_linesr   Zpretty_signr   paddingr<   r<   r=   _print_Product  sH   





$zPrettyPrinter._print_Productc                    s4    fdd}  |d }||d |d }||fS )Nc                    s>   t dtd d } | } |}t t||| }|S )Nr   ==)r   r   rG   r   r   )r   r   r   r   r   rU   rE   r<   r=   print_start.  s
   

z<PrettyPrinter.__print_SumProduct_Limits.<locals>.print_startr   r   r[   rG   )r:   r   r  prettyUpperprettyLowerr<   rE   r=   Z__print_SumProduct_Limits-  s   z'PrettyPrinter.__print_SumProduct_Limitsc                 C   sX  | j  }dd }|j}| |}|jrt|  }| d }d}d}d}	|jD ]n}
| |
\}}t	|| }|||
 |
 |\}}}}td}t|j|  }|rX| }	t|| }t|| }|rz| j|| d |j  8  _d}td}t|jdg|   }t|| }t|| }q(|s|nd}||	d  | |_tj|_|S )	Nc              	   S   s  ddd}t | d}|d }|d }| d }g }	|r|	d| d  |	dd|d    td|D ]}
|	d	d|
 d||
  f  q3|rV|	d
d| d||  f  ttd|D ]}
|	dd|
 d||
  f  q]|	dd|d   d  ||| |	|fS || }|| }tdd}|	d|  td|D ]}
|	dd|
 |d d||
 d  f  qttd|D ]}
|	dd|
 |d d||
 d  f  q|	|d |  ||d|  |	|fS )N<^>c                 S   s|   |rt | |kr
| S |t |  }|dv s|tdvr | d|  S |d }d| }|dkr2d| |  S ||  d|t |   S )N)r  <r  r   r   >)r   r   )r   ZwidhowZneedZhalfleadr<   r<   r=   adjust=  s   z6PrettyPrinter._print_Sum.<locals>.asum.<locals>.adjustr   r[   r   r   z\%s`z%s\%sz%s)%sz%s/%s/r   sumr   r   z%s%s%s   )Nr  )r   r  r   r   r   )Z	hrequiredr   r   Z	use_asciir  r   r   wmorelinesr(   Zvsumr<   r<   r=   asum<  s6   

  
**z&PrettyPrinter._print_Sum.<locals>.asumr   Tr   r   Fr   )rF   r   rG   r   r   rR   r   r   r   r   r   r   r  r   r   r   rb   r   r   )r:   rB   r   r  r   r   r   r   r  r  r   r  r
  r   r   ZslinesZ
adjustmentZ
prettySignpadZascii_adjustmentr<   r<   r=   
_print_Sum9  sF   *


zPrettyPrinter._print_Sumc           	      C   s   |j \}}}}| |}t|td krt|dd }td}| |}| jr0t|d }nt|d }t|| | }t|dksO|t	j
t	jfv rRd}n| jr_t|d	kr]d
nd}t|| | }t|| }t||dtji}|S )Nr   r^   r_   r   u   ─→z->z+-r   +u   ⁺u   ⁻r   )rQ   rG   r   r   r   rR   rF   rb   r6   r   InfinityNegativeInfinityr   r   )	r:   r   rL   zZz0dirEZLimZLimArgr<   r<   r=   _print_Limit  s$   

zPrettyPrinter._print_Limitc                    s  |}i  t |jD ]}t |jD ]| ||f  |f< qq	d}d}dg|j }t |jD ]t fddt |jD pBdg|< q0d}t |jD ]q}d}t |jD ]K |f }	|	 | ksiJ | |	  }
|
d }|
| }t|	d|  }	t|	d|  }	|du r|	}qWt|d|  }t||	 }qW|du r|}qNt |D ]	}t|	d }qt|	| }qN|du rtd	}|S )
zL
        This method factors out what is essentially grid printing.
        r   r[   c                       g | ]
} |f   qS r<   r   .0r(   ZMsr2   r<   r=   
<listcomp>      z8PrettyPrinter._print_matrix_contents.<locals>.<listcomp>r   Nr   r   )
r   rowscolsrG   r   r   r   rb   rS   r   )r:   rL   Mr(   hsepvsepmaxwDD_rowr   wdeltawleftwrightr   r<   r'  r=   _print_matrix_contents  sH   *z$PrettyPrinter._print_matrix_contents[]c                 C   s,   |  |}| d |_t||| }|S )Nr   )r5  r   r   r   rR   )r:   rL   lparensrparensr0  r<   r<   r=   _print_MatrixBase  s   
zPrettyPrinter._print_MatrixBasec                 C   sl   |j }|jr.ddlm} t||r| j|jdddS | |}| d |_	t
|dd S | j|dddS )Nr   )BlockMatrixr   )r8  r9  r   )r   is_MatrixExprZ&sympy.matrices.expressions.blockmatrixr;  r4   r:  blocksrG   r   r   r   rR   )r:   rL   matr;  r0  r<   r<   r=   _print_Determinant  s   

z PrettyPrinter._print_Determinantc                 C   *   | j rd}nd}| j|jd d |dd dS )Nu   ⊗.*c                 S      t | td kS Nr   r   r   r   r<   r<   r=   <lambda>      z4PrettyPrinter._print_TensorProduct.<locals>.<lambda>parenthesizerF   rP   rQ   )r:   rB   Zcircled_timesr<   r<   r=   _print_TensorProduct     z"PrettyPrinter._print_TensorProductc                 C   r@  )Nr   z/\c                 S   rB  rC  rD  rE  r<   r<   r=   rF    rG  z3PrettyPrinter._print_WedgeProduct.<locals>.<lambda>rH  rJ  )r:   rB   Zwedge_symbolr<   r<   r=   _print_WedgeProduct  rL  z!PrettyPrinter._print_WedgeProductc                 C   s<   |  |j}t|dd }| d |_t|d }|S )Nr^   r_   r   tr)rG   r   r   rR   r   r   rS   )r:   rL   r0  r<   r<   r=   _print_Trace  s
   zPrettyPrinter._print_Tracec                 C   s   ddl m} t|j|r%|jjr%|jjr%| t|jj	d|j|jf  S | |j}t
|  }| j|j|jfddjdddd }t
t||d	t
ji}||_||_|S )
Nr   MatrixSymbolz_%d%d, 	delimiterr6  r7  rS   rb   r   )sympy.matricesrQ  r4   parentr(   Z	is_numberr2   rG   r   rW   r   rR   rP   r   r   r   
prettyFunc
prettyArgs)r:   rB   rQ  rX  ZprettyIndicesrU   r<   r<   r=   _print_MatrixElement'  s,   
z"PrettyPrinter._print_MatrixElementc                    s   ddl m}  |j}t|j|st|  } fdd} j||j|jj	||j
|jjfddjddd	d }tt||d
tji}||_||_|S )Nr   rP  c                    sT   t | } | d dkr| d= | d dkrd| d< | d |kr!d| d< t j| dd S )Nr   r[   r   r   :rS  )r   r   rP   )r   dimrE   r<   r=   ppsliceB  s   z1PrettyPrinter._print_MatrixSlice.<locals>.ppslicerR  rS  r6  r7  rU  r   )rV  rQ  rG   rW  r4   r   rR   rP   Zrowslicer*  Zcolslicer+  r   r   r   rX  rY  )r:   mrQ  rX  r]  rY  rU   r<   rE   r=   _print_MatrixSlice<  s,   	
z PrettyPrinter._print_MatrixSlicec                 C   sV   |j }| |}ddlm}m} t||s#t||s#|jr#t|  }|td }|S )Nr   rQ  r;  T)	r   rG   rV  rQ  r;  r4   r<  r   rR   )r:   rB   r>  rU   rQ  r;  r<   r<   r=   _print_TransposeW  s   

zPrettyPrinter._print_Transposec                 C   sj   |j }| |}| jrtd}ntd}ddlm}m} t||s/t||s/|jr/t|	  }|| }|S )Nu   †r  r   r`  )
r   rG   rF   r   rV  rQ  r;  r4   r<  rR   )r:   rB   r>  rU   ZdagrQ  r;  r<   r<   r=   _print_Adjointa  s   


zPrettyPrinter._print_Adjointc                 C   s(   |j jdkr| |j d S | |j S )Nr[   r[   r   r   )r=  shaperG   )r:   Br<   r<   r=   _print_BlockMatrixo  s   z PrettyPrinter._print_BlockMatrixc                 C   s   d }|j D ]8}| |}|d u r|}q| d }t| r-tt|d }| |}ntt|d }tt|| }q|S )Nr   r    + )rQ   rG   Zas_coeff_mmulr   could_extract_minus_signr   r   r   )r:   rB   r   itemrU   coeffr<   r<   r=   _print_MatAddt  s   

zPrettyPrinter._print_MatAddc                 C   s   t |j}ddlm} ddlm} ddlm} t|D ]'\}}t	|t
|||fr;t|jdkr;t| |  ||< q| |||< qtj| S )Nr   HadamardProduct)KroneckerProductMatAddr[   )r   rQ   #sympy.matrices.expressions.hadamardro  Z$sympy.matrices.expressions.kroneckerrp  !sympy.matrices.expressions.mataddrr  	enumerater4   r   r   r   rG   rR   __mul__)r:   rB   rQ   ro  rp  rr  r(   ar<   r<   r=   _print_MatMul  s   

zPrettyPrinter._print_MatMulc                 C      | j rtdS tdS )Nu   𝕀IrF   r   rA   r<   r<   r=   _print_Identity     zPrettyPrinter._print_Identityc                 C   ry  )Nu   𝟘0r{  rA   r<   r<   r=   _print_ZeroMatrix  r}  zPrettyPrinter._print_ZeroMatrixc                 C   ry  )Nu   𝟙1r{  rA   r<   r<   r=   _print_OneMatrix  r}  zPrettyPrinter._print_OneMatrixc                 C   s4   t |j}t|D ]\}}| |||< q	tj| S r?   )r   rQ   ru  rG   r   rv  r:   rB   rQ   r(   rw  r<   r<   r=   _print_DotProduct  s   

zPrettyPrinter._print_DotProductc                 C   sL   |  |j}ddlm} t|j|s|jjrt|  }||  |j }|S )Nr   rP  )	rG   baserV  rQ  r4   r<  r   rR   exp)r:   rB   rU   rQ  r<   r<   r=   _print_MatPow  s   zPrettyPrinter._print_MatPowc                    sZ   ddl m  ddlm ddlm | jrtd}nd}| j|j	d d | fddd	S )
Nr   rn  rq  MatMulRingrA  c                    s   t |  fS r?   r4   rE  ro  rr  r  r<   r=   rF    rG  z6PrettyPrinter._print_HadamardProduct.<locals>.<lambda>rH  )
rs  ro  rt  rr  !sympy.matrices.expressions.matmulr  rF   r   rP   rQ   r:   rB   delimr<   r  r=   _print_HadamardProduct  s   
z$PrettyPrinter._print_HadamardProductc                 C   sp   | j rtd}n| d}| |j}| |j}t|jtd k r(t|  }tt	
||dtji}|| S )Nr  .r   r   )rF   r   rG   r  r  r   r   r   rR   r   r   r   )r:   rB   circZpretty_baseZ
pretty_expZpretty_circ_expr<   r<   r=   _print_HadamardPower  s   


z"PrettyPrinter._print_HadamardPowerc                    sH   ddl m  ddlm | jrd}nd}| j|jd d | fdddS )	Nr   rq  r  u    ⨂ z x c                    s   t |  fS r?   r  rE  rr  r  r<   r=   rF    s    z7PrettyPrinter._print_KroneckerProduct.<locals>.<lambda>rH  )rt  rr  r  r  rF   rP   rQ   r  r<   r  r=   _print_KroneckerProduct  s   z%PrettyPrinter._print_KroneckerProductc                 C   s"   |  |jj}t|dd }|S Nr6  r7  )rG   lamdarB   r   rR   )r:   Xr0  r<   r<   r=   _print_FunctionMatrix  s   z#PrettyPrinter._print_FunctionMatrixc                 C   sP   |j dks|j |j}}t|t|ddddd}| |S | d| |j S )Nr[   r"  Fevaluate)r   denr   r
   
_print_MulrG   )r:   rB   r   r  resr<   r<   r=   _print_TransferFunction  s
   

z%PrettyPrinter._print_TransferFunctionc                 C   s>   t |j}t|jD ]\}}t| |  ||< q
tj| S r?   )r   rQ   ru  r   rG   rR   rv  r  r<   r<   r=   _print_Series  s   

zPrettyPrinter._print_Seriesc                 C   s   ddl m} t|j}g }tt|D ]7\}}t||r9t|jdkr9| |}|	 d |_
|t|   q| |}|	 d |_
|| qtj| S )Nr   )MIMOParallelr[   r   )sympy.physics.control.ltir  r   rQ   ru  r   r4   r   rG   r   r   r  r   rR   rv  )r:   rB   r  rQ   Zpretty_argsr(   rw  Z
expressionr<   r<   r=   _print_MIMOSeries  s   



zPrettyPrinter._print_MIMOSeriesc                 C   sh   d }|j D ],}| |}|d u r|}qtt| }| d |_tt|d }tt|| }q|S )Nr   ri  )rQ   rG   r   r   r   r   r   )r:   rB   r   rk  rU   r<   r<   r=   _print_Parallel  s   

zPrettyPrinter._print_Parallelc                 C   s   ddl m} d }|jD ]8}| |}|d u r|}qtt| }| d |_tt|d }t	||r;| d |_tt|| }q|S )Nr   )TransferFunctionMatrixr   ri  r[   )
r  r  rQ   rG   r   r   r   r   r   r4   )r:   rB   r  r   rk  rU   r<   r<   r=   _print_MIMOParallel  s   


z!PrettyPrinter._print_MIMOParallelc           
      C   s  ddl m}m} |j|dd|j}}t||rt|jn|g}t|j|r,t|jjn|jg}t||rEt|j|rE|g ||R  }nYt||ret|j|re|j|krZ|| }nD|g ||jR  }n9t||rt|j|r||kry|| }n%||g|R  }n||kr|| }n|j|kr|| }n	|g ||R  }t	t
| | }	|	 d |	_|jdkrt	t
|	d nt	t
|	d }	t	t
|	| | }	| ||	 S )Nr   )TransferFunctionSeriesr[   r   r"  ri   - )sympy.physics.controlr  r  sys1varr4   r   rQ   sys2r   r   r   rG   r   r   sign)
r:   rB   r  r  r   tfZnum_arg_listZden_arg_listr  denomr<   r<   r=   _print_Feedback  s:   






zPrettyPrinter._print_Feedbackc                 C   s   ddl m}m} | ||j|j}| |j}tt| }|j	dkr,tt
d| ntt
d| }tt| }d|_tt
|d }| d |_t|td}t|j|rb| d	 |_tt|| }|S )
Nr   )
MIMOSeriesr  r"  zI + zI - z-1 r   r   r[   )r  r  r  rG   r  r  r   r   r   r  rb   rR   r   r   rv  r4   )r:   rB   r  r  Zinv_matZplantZ	_feedbackr<   r<   r=   _print_MIMOFeedback=  s    z!PrettyPrinter._print_MIMOFeedbackc                 C   s>   |  |j}| d |_| jrtd nd}t|| }|S )Nr[   tauz{t})rG   Z	_expr_matr   r   rF   r!   r   rb   )r:   rB   r>  Z	subscriptr<   r<   r=   _print_TransferFunctionMatrixO  s
   z+PrettyPrinter._print_TransferFunctionMatrixc                 C   s  ddl m} | jstd||jkrt|jjS g }g }t||r(| 	 }nd|fg}|D ]M\}}t
|j	 }|jdd d |D ]7\}	}
|
dkrU|d|	j  n |
d	krb|d
|	j  n| |
 d }||d |	j  ||	j qDq/|d dr|d dd  |d< n|d dr|d dd  |d< g }dg}g }t|D ]}\}}|d d|v r(|}||| d}d|v rtt|D ],}d||< || dkr||d  dkr|d | d d ||  ||d d   } nqn)d|v r$|d}|d	kr$d||< |d | d d ||  ||d d   }|||< qdd |D }tdd |D }d|v r_t|D ]\}}t|dkr]|ddt|d   d||< qBt|D ]\}}|t|||   t|D ]}|d t|kr|t|kr|dt|d d	 dt|d     ||| kr|||   |||  d 7  < qv||  || d|d	 t||  d   7  < qv|t|kr|dt|d d	 dt|d     ||  d|d	 d  7  < qvqctddd |D S )Nr   )Vectorz:ASCII pretty printing of BasisDependent is not implementedc                 S   s   | d   S Nr   )__str__rE  r<   r<   r=   rF  f      z5PrettyPrinter._print_BasisDependent.<locals>.<lambda>r   r[   r   r"  z(-1) r   ri  r   
u   ⎟u   ⎠c                 S   s   g | ]}| d qS )r  )splitr&  r   r<   r<   r=   r(        z7PrettyPrinter._print_BasisDependent.<locals>.<listcomp>c                 S   s   g | ]}t |qS r<   )r   r  r<   r<   r=   r(    s    c                 S   s   g | ]}|d d qS )Nr<   )r&  r   r<   r<   r=   r(        )Zsympy.vectorr  rF   NotImplementedErrorzeror   Z_pretty_formr4   Zseparateitemsr   
componentsr   r  rG   rR   
startswithru  r   r   r   rfindr   insertr  join)r:   rB   r  Zo1Zvectstrsr  systemZvectZ
inneritemsr   vZarg_strlengthsstrsflagr(   ZpartstrZtempstrZparenindexZ
n_newlinespartsr2   r<   r<   r=   _print_BasisDependentV  s   








$
 z#PrettyPrinter._print_BasisDependentc           	         sd  ddl m  | dkr| |d S g gdd t| D  }dd |jD } fdd}tj| D ]e}|d	 ||  d
}t| d d	d	D ]M}t	||d  |j| k r\ n=|rj|| ||d   n%|| |||d   t	||d  dkr||| d	 gg|| d	< | }g ||d < qKq4|d d }| d dkr||g}| |S )Nr   ImmutableMatrixr<   c                 S   s   g | ]}g qS r<   r<   r%  r<   r<   r=   r(    rG  z2PrettyPrinter._print_NDimArray.<locals>.<listcomp>c                 S   s   g | ]}t t|qS r<   )r   r   r%  r<   r<   r=   r(    r  c                    s    | ddS )NFr  r<   rE  r  r<   r=   rF    r  z0PrettyPrinter._print_NDimArray.<locals>.<lambda>r"  Tr[   r   )
Zsympy.matrices.immutabler  rankrG   r   rf  	itertoolsproductr  r   )	r:   rB   Z	level_strZshape_rangesr>  Zouter_iZevenZback_outer_iZout_exprr<   r  r=   _print_NDimArray  s8   



zPrettyPrinter._print_NDimArrayc              	   C   sn  t |}t d|  }t d|  }d }d }t|D ]\}	}
| |
jd }|
|v s.|rG||
jkrG|
jr?tt |d }ntt |d }|
|v rctt |d }tt || ||
  }d}nd}|
jrt || }t |d|   }t |d|   }nt || }t |d|   }t |d|   }|
j}qt|	| }t|
| }|S )Nr   r   r   =TF)r   r   ru  rG   rQ   is_upr   r   rb   r   r   )r:   rW   indices	index_mapcentertopbotZlast_valenceZprev_mapr(   r  ZindpicZpictr<   r<   r=   _printer_tensor_indices  s6   z%PrettyPrinter._printer_tensor_indicesc                 C   s    |j d j}| }| ||S r  )rQ   rW   get_indicesr  )r:   rB   rW   r  r<   r<   r=   _print_Tensor   s   zPrettyPrinter._print_Tensorc                 C   s,   |j jd j}|j  }|j}| |||S r  )rB   rQ   rW   r  r  r  )r:   rB   rW   r  r  r<   r<   r=   _print_TensorElement  s   
z"PrettyPrinter._print_TensorElementc                    s>   |  \}} fdd|D }tj| }|rt|| S |S )Nc                    8   g | ]}t |td  k rt |  n |qS r   r   r   r   rG   rR   r%  rE   r<   r=   r(        z0PrettyPrinter._print_TensMul.<locals>.<listcomp>)Z!_get_args_for_traditional_printerr   rv  rS   )r:   rB   r  rQ   rU   r<   rE   r=   _print_TensMul  s   

zPrettyPrinter._print_TensMulc                    s    fdd|j D }tj| S )Nc                    r  r   r  r%  rE   r<   r=   r(    r  z0PrettyPrinter._print_TensAdd.<locals>.<listcomp>)rQ   r   __add__)r:   rB   rQ   r<   rE   r=   _print_TensAdd  s   

zPrettyPrinter._print_TensAddc                 C   s    |j d }|js| }| |S r  )rQ   r  rG   )r:   rB   r   r<   r<   r=   _print_TensorIndex   s   

z PrettyPrinter._print_TensorIndexc           	      C   s   | j rtd}nd}d }t|jD ]#}| |}t|| }|d u r&|}qt|d }t|| }qt| |j	 dtj
i}t|}t|jdkrX|| t|j }t|tj| }|jd |_tt|| }tj|_|S )Nr   r   r   r   r[   )rF   r"   r   	variablesrG   r   rS   rb   rB   rR   r   r   r   r   r   r   r   r   r   )	r:   r   r   r   variabler   r   r   rU   r<   r<   r=   _print_PartialDerivative&  s0   

z&PrettyPrinter._print_PartialDerivativec                    s  i  t |jD ]-\}}| |j |df< |jdkr#td |df< qttd| |j  |df< qd}d}t|j fddtdD }d }tD ]p}d }	tdD ]K}
 ||
f }|	 ||
 ksjJ ||
 |	  }|d }|| }t|d	|  }t|
d	|  }|	d u r|}	qXt|	d	|  }	t|	| }	qX|d u r|	}qPt|D ]	}t|d	 }qt||	 }qPt|d
d }| d |_tj|_|S )Nr   TZ	otherwiser[   zfor r   c                    s(   g | ] t  fd dtD qS )c                    r#  r<   r$  r%  )Pr2   r<   r=   r(  U  r)  z=PrettyPrinter._print_Piecewise.<locals>.<listcomp>.<listcomp>)r   r   r&  r  Zlen_args)r2   r=   r(  U  s     z2PrettyPrinter._print_Piecewise.<locals>.<listcomp>r   {r   )ru  rQ   rG   rB   condr   rb   r   r   r   rS   r   rR   r   r   r   r   )r:   Zpexprr   ecr-  r.  r/  r0  r(   r1  r2   pr2  r3  r4  r   r<   r  r=   _print_PiecewiseF  sP   

zPrettyPrinter._print_Piecewisec                 C   s   ddl m} | ||S )Nr   )	Piecewise)Z$sympy.functions.elementary.piecewiser  rG   Zrewrite)r:   Ziter  r<   r<   r=   
_print_ITE~  s   zPrettyPrinter._print_ITEc                 C   sP   d }|D ]}|}|d u r|}qt |d }t || }q|d u r&td}|S )NrR  r   )r   rb   r   )r:   r  r0  rw  r  r<   r<   r=   _hprint_vec  s   zPrettyPrinter._hprint_vecr   c           	      C   sj   |r| j s| j|d|f|||ddS | j||f|||d}ttd| |jd}| j|||f|||dS )Nr   T)rS   rb   rT  ifascii_nougly)rS   rb   rT  r   )rF   rP   r   r   r   r   )	r:   p1p2rS   rb   rT  r  tmpsepr<   r<   r=   _hprint_vseparator  s   
z PrettyPrinter._hprint_vseparatorc                    s   fdd|j D } fdd|jD } |j}| d |_d }||fD ]} |}|d u r5|}q't|d }t|| }q'| d |_t|	d }t|
d } ||}t|dd }| d d }| | d }	td	\}
}}}}td
||  | d
|	|   ||
 d}|
d d }t|	 t|j  }t|
 t|j }|| |_t|
d| }|S )Nc                       g | ]}  |qS r<   r	  r&  rw  rE   r<   r=   r(    r  z.PrettyPrinter._print_hyper.<locals>.<listcomp>c                    r  r<   r	  r&  brE   r<   r=   r(    r  r   r   r^   r_   r[   Fr  r  )apbqrG   argumentr   r   r  r   r   rS   rb   r  rR   r$   r   )r:   rL   r  r  r  r0  r  r1  r   r   sztr  addimgr   r<   rE   r=   _print_hyper  s8   

zPrettyPrinter._print_hyperc                     s  i } fdd|j D |d<  fdd|jD |d<  fdd|jD |d<  fdd|jD |d	<  |j}| d
 |_i }|D ]} || ||< qCt	d
D ]H}t
|d|f  |d|f  }t	d
D ]0}|||f }	||	  d
 }
||
 |	  }t|	d|
  }	t|	d|  }	|	|||f< qjqSt|d d|d  }t|d }t|d d|d	  }t|| }| d
 |_t|d }t|d } ||}t|dd }| d
 d }| | d }td\}}}}}td||  | d||   || d} t|j} t|j} t|j} t|j }dd }|||\}}|||\}}t|d| }t|d| }|j| d
 }|dkrit|d|  }t|| }||_t|| }|| |_t|d| }|S )Nc                    r  r<   r	  r  rE   r<   r=   r(    r  z0PrettyPrinter._print_meijerg.<locals>.<listcomp>re  c                    r  r<   r	  r  rE   r<   r=   r(    r  )r   r[   c                    r  r<   r	  r  rE   r<   r=   r(    r  )r[   r   c                    r  r<   r	  r  rE   r<   r=   r(    r  rd  r   r   r[   r   z  r^   r_   Gr  r  c                 S   sV   |   |   }|dkr| |fS |dkr| t|d|  fS t| d|   |fS )Nr   r   )r   r   rS   )r  r  diffr<   r<   r=   r    s   z,PrettyPrinter._print_meijerg.<locals>.adjustrR  )anZaotherZbmZbotherrG   r  r   r   r  r   r   r   r   rS   rb   r   r  rR   r$   r   r  r  ) r:   rL   r  r  Zvpidxr(   r/  r2   r   rS   rb   ZD1ZD2r0  r   r   r  r  r  r  r  r   ppZpqpmZpnr  Zpuplhtr  r<   rE   r=   _print_meijerg  sj   "

zPrettyPrinter._print_meijergc                 C   s"   t tdd}|| |jd  S )NExp1rL   r   )r   r   rG   rQ   )r:   rL   r  r<   r<   r=   _print_ExpBase  s   zPrettyPrinter._print_ExpBasec                 C   s   t tddS )Nr  rL   )r   r   rK   r<   r<   r=   _print_Exp1$     zPrettyPrinter._print_Exp1r^   r_   c                 C   s   | j |j|j||||dS )N)r   	func_namerS   rb   )_helper_print_functionrq   rQ   )r:   rL   r   r  rS   rb   r<   r<   r=   r   '  s   zPrettyPrinter._print_Functionc                 C      | j |ddS NCr  r   rK   r<   r<   r=   _print_mathieuc-  r  zPrettyPrinter._print_mathieucc                 C   r  Nr   r  r  rK   r<   r<   r=   _print_mathieus0  r  zPrettyPrinter._print_mathieusc                 C   r  )NzC'r  r  rK   r<   r<   r=   _print_mathieucprime3  r  z"PrettyPrinter._print_mathieucprimec                 C   r  )NzS'r  r  rK   r<   r<   r=   _print_mathieusprime6  r  z"PrettyPrinter._print_mathieusprimerR  c	                 C   s   |rt |td}|st|dr|j}|r| t|}	n	t| |  }	|rB| jr/t	d}
nd}
| |
}
tt
|	|
dtji}	t| j||dj||d }tt
|	|dtji}|	|_||_|S )Nr   rw   zModifier Letter Low Ringr  r   rS  rU  )r   r   hasattrrw   rG   r   r   rR   rF   r   r   r   r   rP   r   rX  rY  )r:   rq   rQ   r   r  rT  elementwiserS   rb   rX  r  rY  rU   r<   r<   r=   r  9  s8   



z$PrettyPrinter._helper_print_functionc                 C   s$   |j }|j}|g}| j||dddS )Nr   T)rT  r#  )r   rB   r  )r:   rL   rq   r   rQ   r<   r<   r=   _print_ElementwiseApplyFunction^  s   z-PrettyPrinter._print_ElementwiseApplyFunctionc                 C   s   ddl m} ddlm}m} ddlm} ddlm} ddl	m
} ddlm} |td dg|td	 d	g|td
 dg|td dg|td dg|td dg|ddgiS )Nr   )KroneckerDelta)gamma
lowergamma)lerchphi)beta)
DiracDelta)ChideltaGammaPhir(  r&  Betarg  r+  )Z(sympy.functions.special.tensor_functionsr%  Z'sympy.functions.special.gamma_functionsr&  r'  Z&sympy.functions.special.zeta_functionsr(  Z&sympy.functions.special.beta_functionsr)  Z'sympy.functions.special.delta_functionsr*  Z'sympy.functions.special.error_functionsr+  r!   )r:   r%  r&  r'  r(  r)  r*  r+  r<   r<   r=   _special_function_classesd  s   z'PrettyPrinter._special_function_classesc                 C   sf   | j D ]&}t||r)|j|jkr)| jrt| j | d   S t| j | d   S q|j}tt|S )Nr   r[   )r0  
issubclassrw   rF   r   r   )r:   rB   clsr  r<   r<   r=   _print_FunctionClasst  s   
z"PrettyPrinter._print_FunctionClassc                 C   
   |  |S r?   )rC   rA   r<   r<   r=   _print_GeometryEntity~  s   
z#PrettyPrinter._print_GeometryEntityc                 C       | j rtd nd}| j||dS )Nr.  r(  r  rF   r!   r   r:   rL   r  r<   r<   r=   _print_lerchphi     zPrettyPrinter._print_lerchphic                 C   r6  )NetaZdirichlet_etar  r7  r8  r<   r<   r=   _print_dirichlet_eta  r:  z"PrettyPrinter._print_dirichlet_etac                 C   sZ   | j rtd nd}|jd tju r&t| |jd   }t|| }|S | j	||dS )NthetaZ	Heavisider[   r   r  )
rF   r!   rQ   r   ZHalfr   rG   rR   rS   r   )r:   rL   r  rU   r<   r<   r=   _print_Heaviside  s   zPrettyPrinter._print_Heavisidec                 C   r  r  r  rK   r<   r<   r=   _print_fresnels  r  zPrettyPrinter._print_fresnelsc                 C   r  r  r  rK   r<   r<   r=   _print_fresnelc  r  zPrettyPrinter._print_fresnelcc                 C   r  )NZAir  r  rK   r<   r<   r=   _print_airyai  r  zPrettyPrinter._print_airyaic                 C   r  )NZBir  r  rK   r<   r<   r=   _print_airybi  r  zPrettyPrinter._print_airybic                 C   r  )NzAi'r  r  rK   r<   r<   r=   _print_airyaiprime  r  z PrettyPrinter._print_airyaiprimec                 C   r  )NzBi'r  r  rK   r<   r<   r=   _print_airybiprime  r  z PrettyPrinter._print_airybiprimec                 C   r  )NWr  r  rK   r<   r<   r=   _print_LambertW  r  zPrettyPrinter._print_LambertWc                 C   r  )NZCovr  r  rK   r<   r<   r=   _print_Covariance  r  zPrettyPrinter._print_Covariancec                 C   r  )NZVarr  r  rK   r<   r<   r=   _print_Variance  r  zPrettyPrinter._print_Variancec                 C   r  )Nr  r  r  rK   r<   r<   r=   _print_Probability  r  z PrettyPrinter._print_Probabilityc                 C   s   | j |ddddS )Nr   r6  r7  )r  rS   rb   r  rK   r<   r<   r=   _print_Expectation  s   z PrettyPrinter._print_Expectationc                 C   sb   |j }|j}| jrd}nd}t|dkr|d jr|d }| |}tt||| |ddiS )Nu    ↦  -> r[   r   r   r  )	rB   	signaturerF   r   Z	is_symbolrG   r   r   r   )r:   rL   rB   sigarrowZvar_formr<   r<   r=   _print_Lambda  s   
zPrettyPrinter._print_Lambdac                 C   s  |  |j}|jrtdd |jD st|jdkrxt|d }t|jdkr4t||  |j }nt|jrFt||  |jd  }| jrQt|d }nt|d }t|jdkrkt||  |j }nt||  |jd  }t|	  }t|
d }|S )	Nc                 s   s    | ]}|t jkV  qd S r?   )r   Zero)r&  r  r<   r<   r=   	<genexpr>      z-PrettyPrinter._print_Order.<locals>.<genexpr>r[   ; r   u    → rK  O)rG   rB   pointanyr   r  r   rb   rF   rR   rS   r:   rB   rU   r<   r<   r=   _print_Order  s"   
zPrettyPrinter._print_Orderc                 C   s   | j r0| |jd |jd  }| |jd }td}t|| }t|d }|| }|S | |jd }| |jd |jd  }| |ddd}|| S )Nr   r[   r   r  r  r   )rF   rG   rQ   r   rb   rP   )r:   rL   shiftr   r  rU   r<   r<   r=   _print_SingularityFunction  s   z(PrettyPrinter._print_SingularityFunctionc                 C   r6  )Nr/  rg  r  r7  r8  r<   r<   r=   _print_beta  r:  zPrettyPrinter._print_betac                 C      d}| j ||dS )NzB'r  r  r8  r<   r<   r=   _print_betainc     zPrettyPrinter._print_betaincc                 C   r\  )Nrz  r  r  r8  r<   r<   r=   _print_betainc_regularized  r^  z(PrettyPrinter._print_betainc_regularizedc                 C       | j rtd nd}| j||dS Nr-  r  r7  r8  r<   r<   r=   _print_gamma  r:  zPrettyPrinter._print_gammac                 C   r`  ra  r7  r8  r<   r<   r=   _print_uppergamma  r:  zPrettyPrinter._print_uppergammac                 C   r6  )Nr&  r'  r  r7  r8  r<   r<   r=   _print_lowergamma  r:  zPrettyPrinter._print_lowergammac                 C   s   | j rYt|jdkr@ttd }| |jd }t|  }| |jd }t|  }|| }t|d }t|| }|S | |jd }t|  }t|td  }|S | 	|S )Nr   r,  r[   r   r   )
rF   r   rQ   r   r!   rG   rR   rb   rS   r   )r:   rL   rw  r  crU   r<   r<   r=   _print_DiracDelta  s    
zPrettyPrinter._print_DiracDeltac                 C   s>   |j d jr| jr| td|j d  |j d S | |S )Nr   zE_%sr[   )rQ   r~   rF   r   r   rK   r<   r<   r=   _print_expint  s   "
zPrettyPrinter._print_expintc                 C   sD   t d}t | |j  }t t||dt ji}||_||_|S )Nr+  r   )	r   rP   rQ   rR   r   r   r   rX  rY  )r:   rL   rX  rY  rU   r<   r<   r=   
_print_Chi  s   
zPrettyPrinter._print_Chic                 C   s^   |  |jd }t|jdkr|}n|  |jd }| ||}t|  }t|d }|S )Nr   r[   r   )rG   rQ   r   r  r   rR   rS   )r:   rL   pforma0rU   pforma1r<   r<   r=   _print_elliptic_e$  s   zPrettyPrinter._print_elliptic_ec                 C   s.   |  |jd }t|  }t|d }|S )Nr   K)rG   rQ   r   rR   rS   rT   r<   r<   r=   _print_elliptic_k/  s   zPrettyPrinter._print_elliptic_kc                 C   sJ   |  |jd }|  |jd }| ||}t|  }t|d }|S )Nr   r[   r   )rG   rQ   r  r   rR   rS   )r:   rL   ri  rj  rU   r<   r<   r=   _print_elliptic_f5  s   zPrettyPrinter._print_elliptic_fc                 C   s   | j rtd nd}| |jd }| |jd }t|jdkr'| ||}n| |jd }| j||dd}t|d }t|| }t|  }t|| }|S )NPir   r[   r   Fr  rS  )	rF   r!   rG   rQ   r   r  r   rS   rR   )r:   rL   rW   ri  rj  rU   Zpforma2Zpformar<   r<   r=   _print_elliptic_pi=  s   z PrettyPrinter._print_elliptic_pic                 C       | j r	ttdS | tdS )NphiZGoldenRatiorF   r   r   rG   r   rA   r<   r<   r=   _print_GoldenRatioL     z PrettyPrinter._print_GoldenRatioc                 C   rr  )Nr&  Z
EulerGammart  rA   r<   r<   r=   _print_EulerGammaQ  rv  zPrettyPrinter._print_EulerGammac                 C   s   |  tdS )Nr	  )rG   r   rA   r<   r<   r=   _print_CatalanV  r  zPrettyPrinter._print_Catalanc                 C   s\   |  |jd }|jtjkrt|  }t|d }t||  |jd  }tj|_|S )Nr   z mod r[   )rG   rQ   r   r   r   rR   rb   r   rW  r<   r<   r=   
_print_ModY  s   zPrettyPrinter._print_Modc                 C   s  | j ||d}g g }}dd }t|D ]z\}}|jrM| rM|jdd\}	}
|	dkr3t|
ddi}nt|	 g|
R ddi}| |}|||| q|jr`|j	dkr`|d  || q|j
rv|d	k rv| | }|||| q|jr|t| |   q|| | q|rd
}|D ]}|d ur| dkr nqd}|D ]4}|| d}}|d	k r| d
}}|rtt|jtt|j	 }n| |}|r|||}|||< qtj| S )Nr)   c                 S   sj   |dkr|   dkrd}nd}nd}| jtjks| jtjkr%t|   }n| }t||}t|dtjiS )z'Prepend a minus sign to a pretty form. r   r[   z- r   r  r   )r   r   r   NEGZADDr   rR   r   )rU   r  Z	pform_negr  r<   r<   r=   pretty_negativef  s   z1PrettyPrinter._print_Add.<locals>.pretty_negativeF)Zrationalr"  r  r[   r   T)Z_as_ordered_termsru  Zis_Mulrj  Zas_coeff_mulr   rG   r  is_RationalqZ	is_Numberis_Relationalr   rR   r   r6   r  r  )r:   rB   r)   Ztermspformsr  r|  r(   r   rl  otherZnegtermrU   Zlargenegativer<   r<   r=   
_print_Addb  sL   






zPrettyPrinter._print_Addc           	         s  ddl m  |j}|d tju stdd |dd  D rIttj|}|d dk}|r5t	ddd|d< t	j
| }|rGt	d|j |j|j}|S g }g }jd	vrW| }nt|j}t| fd
dd}|D ]W}|jr|jr|jjr|jjr|jdkr|t|j|j dd qh|t|j|j  qh|jr|tjur|jdkr|t|j |jdkr|t|j qh|| qhfdd|D }fdd|D }t|dkrt	j
| S t|dkr|tj t	j
| t	j
|  S )Nr   Quantityc                 s   s    | ]}t |tV  qd S r?   )r4   r   r&  r   r<   r<   r=   rQ    rR  z+PrettyPrinter._print_Mul.<locals>.<genexpr>r[   z-1r  r   )oldnonec                    s    t |  pt | tot | j S r?   )r4   r
   r  rE  r  r<   r=   rF    s   
 z*PrettyPrinter._print_Mul.<locals>.<lambda>r   r"  Fr  c                    r  r<   r	  )r&  ZairE   r<   r=   r(    r  z,PrettyPrinter._print_Mul.<locals>.<listcomp>c                    r  r<   r	  )r&  ZbirE   r<   r=   r(    r  )Zsympy.physics.unitsr  rQ   r   OnerV  r   maprG   r   rv  r   r   r   r)   Zas_ordered_factorsr   is_commutativeZis_Powr  r}  Zis_negativer  r
   r  r  r  r	   r~  r   )	r:   r  rQ   ZstrargsZnegoneobjrw  r  rk  r<   )r  r:   r=   r    sH   (







zPrettyPrinter._print_Mulc           	         st  |  |}| jd r*| jr*|dkr*| dkr*| dks#|jr*|jr*t|d S t	dd t	dd  }|  |}| dkrM|  ||  d|  S |dkrSdnt
|d}t|dkrjdt|d  | }t|d	 | }d
|_| d td	 fddtD }d |_t|| }td|j|_ttdd|  }t|| }t|| }|S )Nr-   r   r[   u   √r  \r   r   r  r   c                 3   s,    | ]}d | d    d |  V  qdS )r   r[   Nr<   r%  Z_zZZ
linelengthr<   r=   rQ    s
    
z0PrettyPrinter._print_nth_root.<locals>.<genexpr>r   )rG   r5   rF   r   r   r~   r   r   rS   r   r6   ljustr   r   r   r  r   rb   r   r   r   )	r:   r  rootZbprettyZrootsignZrprettyr  Zdiagonalr   r<   r  r=   _print_nth_root  s<   




zPrettyPrinter._print_nth_rootc                 C   s   ddl m} | \}}|jrU|tju rtd| | S ||\}}|tju r?|j	r?|j
s?|js4|jr?| jd r?| ||S |jrU|dk rUtd| t|| dd S |jrgt| |  | |S | || | S )Nr   )fractionr  r.   Fr  )Zsympy.simplify.simplifyr  Zas_base_expr  r   ZNegativeOner   rG   r  Zis_Atomr~   r}  r   r5   r  r
   r  rR   __pow__)r:   powerr  r  rL   r   r   r<   r<   r=   
_print_Pow  s   
"zPrettyPrinter._print_Powc                 C   s   |  |jd S r  )rG   rQ   rA   r<   r<   r=   _print_UnevaluatedExpr%     z$PrettyPrinter._print_UnevaluatedExprc                 C   s   |dkr|dk rt t|t jdS t t|S t|dkrBt|dkrB|dk r6t t|t jdt t| S t t|t t| S d S )Nr[   r   )r   
   )r   r6   r{  abs)r:   r  r~  r<   r<   r=   Z__print_numer_denom(  s   z!PrettyPrinter.__print_numer_denomc                 C   &   |  |j|j}|d ur|S | |S r?   )!_PrettyPrinter__print_numer_denomr  r~  rC   r:   rB   r   r<   r<   r=   _print_Rational:     
zPrettyPrinter._print_Rationalc                 C   r  r?   )r  	numeratordenominatorrC   r  r<   r<   r=   _print_FractionB  r  zPrettyPrinter._print_Fractionc                 C   sd   t |jdkrt|js| |jd | t |j S | jr!dnd}| j|jd d d| dd dS )	Nr[   r      ×r   r   c                 S      | j p| jp| jS r?   )is_Unionis_Intersectionis_ProductSetsetr<   r<   r=   rF  P      z1PrettyPrinter._print_ProductSet.<locals>.<lambda>rH  )r   setsr   rG   rF   rP   )r:   r  Z	prod_charr<   r<   r=   _print_ProductSetJ  s    zPrettyPrinter._print_ProductSetc                 C   s   t |jtd}| |dddS )Nr   r  }rR  )r   rQ   r   rP   )r:   r   r  r<   r<   r=   _print_FiniteSetS  s   zPrettyPrinter._print_FiniteSetc                 C   s   | j rd}nd}|jjr$|jjr$|jjr|ddd|f}nF|ddd|f}n>|jjr5||d |j |d f}n-|jjrGt|}t|t||f}nt|dkr^t|}t|t|||d f}nt	|}| 
|ddd	S )
N   …...r"  r   r[   r   r  r  rR  )rF   startis_infinitestopstepZis_positiveiterr   r   r   rP   )r:   r   dotsprintsetitr<   r<   r=   _print_RangeW  s"   zPrettyPrinter._print_Rangec                 C   s\   |j |jkr| |jd d ddS |jrd}nd}|jr d}nd}| |jd d ||S )	Nr[   r  r  r^   r6  r_   r7  r   )r  endrP   rQ   Z	left_openZ
right_openr:   r(   rS   rb   r<   r<   r=   _print_Intervalp  s   zPrettyPrinter._print_Intervalc                 C   s    d}d}|  |jd d ||S )Nr  r  r   rP   rQ   r  r<   r<   r=   _print_AccumulationBounds  s   z'PrettyPrinter._print_AccumulationBoundsc                 C   (   dt dd }| j|jd d |dd dS )Nr   ZIntersectionr   c                 S   r  r?   )r  r  is_Complementr  r<   r<   r=   rF    r  z3PrettyPrinter._print_Intersection.<locals>.<lambda>rH  r   rP   rQ   r:   r   rT  r<   r<   r=   _print_Intersection     z!PrettyPrinter._print_Intersectionc                 C   r  )Nr   Unionr"   c                 S   r  r?   )r  r  r  r  r<   r<   r=   rF    r  z,PrettyPrinter._print_Union.<locals>.<lambda>rH  r  )r:   r   Zunion_delimiterr<   r<   r=   _print_Union  r  zPrettyPrinter._print_Unionc                 C   s,   | j stddtd }| |jd d |S )Nz?ASCII pretty printing of SymmetricDifference is not implementedr   ZSymmetricDifference)rF   r  r   rP   rQ   )r:   r   Zsym_delimeterr<   r<   r=   _print_SymmetricDifference  s   z(PrettyPrinter._print_SymmetricDifferencec                 C   s   d}| j |jd d |dd dS )Nz \ c                 S   r  r?   )r  r  r  r  r<   r<   r=   rF    s    z1PrettyPrinter._print_Complement.<locals>.<lambda>rH  r  r  r<   r<   r=   _print_Complement  s   zPrettyPrinter._print_Complementc                    s   | j rd nd |j}|j}|j}| |j}t|dkr6| j|d  |d fdd}| j||ddd	dd
S t	 fddt
||D }| j|d d dd}| j||ddd	dd
S )N   ∊inr[   r   r   rS  r  r  TrS   rb   r  rT  c                 3   s.    | ]\}}|d  d |dfD ]}|V  qqdS )r   rR  Nr<   )r&  r  Zsetvr2   innr<   r=   rQ    s   
 z0PrettyPrinter._print_ImageSet.<locals>.<genexpr>r"  r   )rF   r  Z	base_setsrL  rG   rB   r   rP   r  r   r   )r:   tsfunr  rL  rB   r   Zpargsr<   r  r=   _print_ImageSet  s*   zPrettyPrinter._print_ImageSetc           	      C   s   | j rd}d}nd}d}| t|j}t|jdd }|d ur(| |j }n| |j}| j r<| |}t|	  }|j
tju rM| j||dddd	d
S | |j
}| j|||||fd	d}| j||dddd	d
S )Nr  r   r  andas_exprr  r  Tr   r  rS  )rF   rP   r   r   getattr	conditionrG   r  r   rR   Zbase_setr   UniversalSetr  )	r:   r  r  Z_andr  r  r  r  r  r<   r<   r=   _print_ConditionSet  s2   

z!PrettyPrinter._print_ConditionSetc                 C   s^   | j rd}nd}| |j}| |j}| |j}| j|||fdd}| j||dddddS )	Nr  r  r   rS  r  r  Tr  )rF   rP   r  rG   rB   r  r  )r:   r  r  r  rB   Zprodsetsr  r<   r<   r=   _print_ComplexRegion  s   z"PrettyPrinter._print_ComplexRegionc                 C   sD   |j \}}| jrd}tt| ||| |ddiS tt|S )Nu    ∈ r   r  )rQ   rF   r   r   r   rG   r   )r:   rL   r  r  elr<   r<   r=   _print_Contains  s   

zPrettyPrinter._print_Containsc                 C   sP   |j jtju r|jjtju r| |jS | jrd}nd}| |	 | | S )Nr  r  )
r  Zformular   rP  ZbnrG   Za0rF   r  truncate)r:   r   r  r<   r<   r=   _print_FourierSeries  s   z"PrettyPrinter._print_FourierSeriesc                 C      |  |jS r?   )r  Zinfiniter:   r   r<   r<   r=   _print_FormalPowerSeries	  rD   z&PrettyPrinter._print_FormalPowerSeriesc                 C   s0   t | |j  }| td}t || S )NZSetExpr)r   rG   r  rR   r   rb   )r:   seZ
pretty_setpretty_namer<   r<   r=   _print_SetExpr	  s   zPrettyPrinter._print_SetExprc                 C   s   | j rd}nd}t|jjdkst|jjdkrtd|jtju r?|j}|||d ||d ||d ||f}n|jtj	u sJ|j
dkrZ|d d }|| t|}nt|}| |S )	Nr  r  r   z@Pretty printing of sequences with symbolic bound not implementedr   r   r[   r   )rF   r   r  Zfree_symbolsr  r  r   r  rl  r  lengthr  r   _print_list)r:   r   r  r  r  r<   r<   r=   _print_SeqFormula	  s     


zPrettyPrinter._print_SeqFormulac                 C   s   dS )NFr<   rE  r<   r<   r=   rF  %	  s    zPrettyPrinter.<lambda>c              	   C   s   z2g }|D ]}|  |}	||rt|	  }	|r|| ||	 q|s*td}
nttj|  }
W n> typ   d }
|D ](}| |}	||rNt|	  }	|
d u rU|	}
q=tt|
| }
tt|
|	 }
q=|
d u rntd}
Y nw t|
j|||d }
|
S )Nr   rp  )rG   r   rR   r  r   r   AttributeErrorrI   )r:   seqrS   rb   rT  rI  r  r  rk  rU   r   r<   r<   r=   rP   $	  s:   



zPrettyPrinter._print_seqc                 C   sL   d }|D ]}|d u r|}qt || }t || }q|d u r$t dS |S )Nr   )r   rb   )r:   rT  rQ   rU   r   r<   r<   r=   r  M	  s   zPrettyPrinter.joinc                 C      |  |ddS r  rP   )r:   r   r<   r<   r=   r  \	  r  zPrettyPrinter._print_listc                 C   sH   t |dkrtt| |d d }t|jdddd S | |ddS )Nr[   r   r   r^   r_   Trp  )r   r   r   r   rG   rR   rP   )r:   r  Zptupler<   r<   r=   _print_tuple_	  s   zPrettyPrinter._print_tuplec                 C   r4  r?   )r  rA   r<   r<   r=   _print_Tuplef	     
zPrettyPrinter._print_Tuplec                 C   s`   t | td}g }|D ]}| |}| || }tt|d| }|| q| |ddS )Nr   z: r  r  )	r   keysr   rG   r   r   r   r  rP   )r:   r   r  r  r   rl  Vr   r<   r<   r=   _print_dicti	  s   
zPrettyPrinter._print_dictc                 C   r4  r?   )r  )r:   r   r<   r<   r=   _print_Dictv	  r  zPrettyPrinter._print_Dictc                 C   s:   |st dS t|td}| |}t |jdddd }|S )Nzset()r   r  r  Trp  )r   r   r   rP   rR   r:   r   r  prettyr<   r<   r=   
_print_sety	  s   
zPrettyPrinter._print_setc                 C   sd   |st dS t|td}| |}t |jdddd }t |jdddd }t tt|j| }|S )	Nzfrozenset()r   r  r  Trp  r^   r_   )	r   r   r   rP   rR   r   r   typerw   r  r<   r<   r=   _print_frozenset	  s   
zPrettyPrinter._print_frozensetc                 C   ry  )Nu   𝕌r  r{  r  r<   r<   r=   _print_UniversalSet	  r}  z!PrettyPrinter._print_UniversalSetc                 C   r>   r?   r   r   )r:   ringr<   r<   r=   _print_PolyRing	  rD   zPrettyPrinter._print_PolyRingc                 C   r>   r?   r  )r:   fieldr<   r<   r=   _print_FracField	  rD   zPrettyPrinter._print_FracFieldc                 C   r>   r?   r@   )r:   elmr<   r<   r=   _print_FreeGroupElement	  rD   z%PrettyPrinter._print_FreeGroupElementc                 C   r>   r?   r  )r:   Zpolyr<   r<   r=   _print_PolyElement	  rD   z PrettyPrinter._print_PolyElementc                 C   r>   r?   r  )r:   fracr<   r<   r=   _print_FracElement	  rD   z PrettyPrinter._print_FracElementc                 C   s&   |j r| |  S | | S r?   )Z
is_aliasedrG   Zas_polyr  rA   r<   r<   r=   _print_AlgebraicNumber	  s   z$PrettyPrinter._print_AlgebraicNumberc                 C   s:   | j |jdd|jg}t| |  }t|d }|S )Nlexrz  ZCRootOf)r  rB   r  r   rP   rR   rS   r:   rB   rQ   rU   r<   r<   r=   _print_ComplexRootOf	  s   z"PrettyPrinter._print_ComplexRootOfc                 C   sT   | j |jddg}|jtjur|| |j t| |	  }t|
d }|S )Nr   rz  ZRootSum)r  rB   r  r   ZIdentityFunctionr  rG   r   rP   rR   rS   r  r<   r<   r=   _print_RootSum	  s   zPrettyPrinter._print_RootSumc                 C   s"   | j rd}nd}tt||j S )Nu   ℤ_%dzGF(%d))rF   r   r   mod)r:   rB   formr<   r<   r=   _print_FiniteField	  s   z PrettyPrinter._print_FiniteFieldc                 C   ry  )Nu   ℤZZZr{  rA   r<   r<   r=   _print_IntegerRing	  r}  z PrettyPrinter._print_IntegerRingc                 C   ry  )Nu   ℚZQQr{  rA   r<   r<   r=   _print_RationalField	  r}  z"PrettyPrinter._print_RationalFieldc                 C   :   | j rd}nd}|jrt|S | t|d t|j S )Nu   ℝZRRr   rF   Zhas_default_precisionr   rG   r   r6   	precisionr:   domainprefixr<   r<   r=   _print_RealField	     zPrettyPrinter._print_RealFieldc                 C   r	  )Nu   ℂZCCr   r
  r  r<   r<   r=   _print_ComplexField	  r  z!PrettyPrinter._print_ComplexFieldc                 C   ^   t |j}|jjsttd| |j }|| | |dd}t|	| |j
 }|S Norder=r6  r7  r   symbolsr)   
is_defaultr   rb   rG   r  rP   rS   r  r:   rB   rQ   r)   rU   r<   r<   r=   _print_PolynomialRing	     

z#PrettyPrinter._print_PolynomialRingc                 C   r  )Nr  r^   r_   r  r  r<   r<   r=   _print_FractionField	  r  z"PrettyPrinter._print_FractionFieldc                 C   sV   |j }t|jt|jkr|dt|j f }| |dd}t|| |j }|S r  )	r  r6   r)   Zdefault_orderrP   r   rS   rG   r  )r:   rB   grU   r<   r<   r=   _print_PolynomialRingBase	  s   z'PrettyPrinter._print_PolynomialRingBasec                    s    fdd j D }td|jddd }fdd jD }ttd j }ttd	 j }d|g| ||g }t|  }t|	 j
j }|S )
Nc                    s   g | ]
}j | jd qS )rz  )r  r)   r  basisr:   r<   r=   r(  
  s    z6PrettyPrinter._print_GroebnerBasis.<locals>.<listcomp>rR  r6  r7  rU  c                    r  r<   r	  )r&  genrE   r<   r=   r(  
  r  zdomain=r  )exprsr   r  rR   gensrb   rG   r  r)   rS   rv   rw   )r:   r  r!  r"  r  r)   rU   r<   r  r=   _print_GroebnerBasis
  s   z"PrettyPrinter._print_GroebnerBasisc              	      s     |j}t|  }| dkr| nd}ttd||jd}t|| }|j}| d |_t| 	 fddt
|j|jD  }||_|S )Nr[   r   r   r  c              	      s8   g | ]} j  |d  td |d fddqS )r   r  r[   r   rS  )rP   rG   r   )r&  r  rE   r<   r=   r(  
  s    $z-PrettyPrinter._print_Subs.<locals>.<listcomp>)rG   rB   r   rR   r   r   r   r   rb   rP   r   r  rU  )r:   rL   rU   r   Zrvertr  r<   rE   r=   _print_Subs
  s   zPrettyPrinter._print_Subsc           
      C   s   t |}| |jd }t d|  }t || }t || }t|jdkr+|S |j\}}|}t | |g  }	t t	
||	dt ji}||_|	|_|S )Nr   r   r[   r   )r   rG   rQ   r   r   rb   r   rP   rR   r   r   r   rX  rY  )
r:   rL   rW   rU   r   r   r^  r   rX  rY  r<   r<   r=   _print_number_function&
  s$   

z$PrettyPrinter._print_number_functionc                 C      |  |dS )Nr   r%  rK   r<   r<   r=   _print_euler:
  rD   zPrettyPrinter._print_eulerc                 C   r&  )Nr  r'  rK   r<   r<   r=   _print_catalan=
  rD   zPrettyPrinter._print_catalanc                 C   r&  )Nrg  r'  rK   r<   r<   r=   _print_bernoulli@
  rD   zPrettyPrinter._print_bernoullic                 C   r&  )NLr'  rK   r<   r<   r=   _print_lucasE
  rD   zPrettyPrinter._print_lucasc                 C   r&  )Nr   r'  rK   r<   r<   r=   _print_fibonacciH
  rD   zPrettyPrinter._print_fibonaccic                 C   r&  )Nra  r'  rK   r<   r<   r=   _print_tribonacciK
  rD   zPrettyPrinter._print_tribonaccic                 C   s   | j r	| |dS | |dS )Nu   γZ	stieltjes)rF   r%  rK   r<   r<   r=   _print_stieltjesN
  s   zPrettyPrinter._print_stieltjesc                 C   s   |  |jd }t|td }t||  |jd  }| jr(ttd}ntd}|}t|d|   }t|d|   }t|	|dtj
iS )Nr   r   r[   r,  r   r   r   )rG   rQ   r   rb   rF   r   r   rS   r   r   ZPOW)r:   rL   rU   rw  r  r  r  r<   r<   r=   _print_KroneckerDeltaT
  s   z#PrettyPrinter._print_KroneckerDeltac                 C   s   t |dr| d}t|| |  }|S t |drD| d}t|| |j }t|| d }t|| |j }|S t |dr[| d}t|| |j }|S | d S )N
as_booleanzDomain: r  z in r  z
Domain on )r"  rG   r   rb   r1  r  r  )r:   r   rU   r<   r<   r=   _print_RandomDomaina
  s   






z!PrettyPrinter._print_RandomDomainc                 C   sD   z|j d ur| |j |W S W n	 ty   Y nw | t|S r?   )r  rG   Zto_sympyr   reprr:   r  r<   r<   r=   
_print_DMPs
  s   
zPrettyPrinter._print_DMPc                 C   r4  r?   )r5  r4  r<   r<   r=   
_print_DMF|
  r  zPrettyPrinter._print_DMFc                 C      |  t|jS r?   rG   r   rW   )r:   objectr<   r<   r=   _print_Object
  r  zPrettyPrinter._print_Objectc                 C   s8   t d}| |j}| |j}|||d }t|S )Nz-->r   )r   rG   r  codomainrb   r   )r:   morphismrN  r  r;  tailr<   r<   r=   _print_Morphism
  s
   zPrettyPrinter._print_Morphismc                 C   s.   |  t|j}| |}t|d|d S )Nr[  r   )rG   r   rW   r>  r   rb   )r:   r<  r  pretty_morphismr<   r<   r=   _print_NamedMorphism
  s   
z"PrettyPrinter._print_NamedMorphismc                 C   s"   ddl m} | ||j|jdS )Nr   )NamedMorphismid)Zsympy.categoriesrA  r@  r  r;  )r:   r<  rA  r<   r<   r=   _print_IdentityMorphism
  s   z%PrettyPrinter._print_IdentityMorphismc                 C   sT   t d}dd |jD }|  ||d }| |}| |}t||d S )Nr  c                 S   s   g | ]}t |jqS r<   )r   rW   )r&  	componentr<   r<   r=   r(  
  s    z:PrettyPrinter._print_CompositeMorphism.<locals>.<listcomp>r[  r   )r   r  reverser  rG   r>  r   rb   )r:   r<  circleZcomponent_names_listZcomponent_namesr  r?  r<   r<   r=   _print_CompositeMorphism
  s   

z&PrettyPrinter._print_CompositeMorphismc                 C   r7  r?   r8  )r:   categoryr<   r<   r=   _print_Category
  r  zPrettyPrinter._print_Categoryc                 C   sX   |j s	| tjS | |j }|jr&dtd }| |jd }|||}t|d S )Nr   z==>r   )ZpremisesrG   r   ZEmptySetZconclusionsr   rb   r   )r:   diagramZpretty_resultZresults_arrowZpretty_conclusionsr<   r<   r=   _print_Diagram
  s   zPrettyPrinter._print_Diagramc                    s2   ddl m} | fddt jD }| |S )Nr   )Matrixc                    s&   g | ]  fd dt jD qS )c                    s,   g | ]} |f r |f nt d qS )r   r   )r&  r2   )gridr(   r<   r=   r(  
  s    $z?PrettyPrinter._print_DiagramGrid.<locals>.<listcomp>.<listcomp>)r   r   r  rM  )r(   r=   r(  
  s
    
z4PrettyPrinter._print_DiagramGrid.<locals>.<listcomp>)rV  rL  r   r   r5  )r:   rM  rL  matrixr<   rN  r=   _print_DiagramGrid
  s
   
z PrettyPrinter._print_DiagramGridc                 C   r  r  r  r:   r^  r<   r<   r=   _print_FreeModuleElement
  s   z&PrettyPrinter._print_FreeModuleElementc                 C   s   |  |jddS )Nr  r  )rP   r"  r:   r,  r<   r<   r=   _print_SubModule
  r  zPrettyPrinter._print_SubModulec                 C   s   |  |j|  |j S r?   )rG   r  r  rS  r<   r<   r=   _print_FreeModule
  rJ   zPrettyPrinter._print_FreeModulec                 C   s   |  dd |jjD ddS )Nc                 S   s   g | ]\}|qS r<   r<   r  r<   r<   r=   r(  
  s    z?PrettyPrinter._print_ModuleImplementedIdeal.<locals>.<listcomp>r  r  )rP   _moduler"  rS  r<   r<   r=   _print_ModuleImplementedIdeal
  s   z+PrettyPrinter._print_ModuleImplementedIdealc                 C      |  |j|  |j S r?   )rG   r  
base_idealr:   Rr<   r<   r=   _print_QuotientRing
  rJ   z!PrettyPrinter._print_QuotientRingc                 C      |  |j|  |jj S r?   )rG   datar  rY  rZ  r<   r<   r=   _print_QuotientRingElement
     z(PrettyPrinter._print_QuotientRingElementc                 C   r]  r?   )rG   r^  modulekilled_modulerQ  r<   r<   r=   _print_QuotientModuleElement
  r`  z*PrettyPrinter._print_QuotientModuleElementc                 C   rX  r?   )rG   r  rb  rS  r<   r<   r=   _print_QuotientModule
  rJ   z#PrettyPrinter._print_QuotientModulec              	   C   sN   |  | }| d |_t|d|  |jdtdd |  |j }|S )Nr   z : z %s> r   )	rG   Z_sympy_matrixr   r   r   rb   r  r   r;  )r:   r   rO  rU   r<   r<   r=   _print_MatrixHomomorphism
  s   z'PrettyPrinter._print_MatrixHomomorphismc                 C   r  r?   rG   rW   )r:   Zmanifoldr<   r<   r=   _print_Manifold
  rD   zPrettyPrinter._print_Manifoldc                 C   r  r?   rf  )r:   patchr<   r<   r=   _print_Patch
  rD   zPrettyPrinter._print_Patchc                 C   r  r?   rf  )r:   coordsr<   r<   r=   _print_CoordSystem
  rD   z PrettyPrinter._print_CoordSystemc                 C   s   |j j|j j}| t|S r?   )
_coord_sysr  _indexrW   rG   r   )r:   r  stringr<   r<   r=   _print_BaseScalarField
  s   z$PrettyPrinter._print_BaseScalarFieldc                 C   s*   t dd |jj|j j }| t|S )Nr   r   )r"   rl  r  rm  rW   rG   r   )r:   r  r   r<   r<   r=   _print_BaseVectorField
  s   z$PrettyPrinter._print_BaseVectorFieldc                 C   sj   | j rd}nd}|j}t|dr#|jj|j j}| |d t| S | |}t	|
  }t	|| S )Nu   ⅆr   rl  r   )rF   Z_form_fieldr"  rl  r  rm  rW   rG   r   r   rR   rS   )r:   r
  r   r  rn  rU   r<   r<   r=   _print_Differential
  s   

z!PrettyPrinter._print_Differentialc                 C   s8   |  |jd }t|d|jj  }t|d }|S )Nr   z%s(r_   )rG   rQ   r   rS   rv   rw   rb   )r:   r  rU   r<   r<   r=   	_print_Tr
  s   zPrettyPrinter._print_Trc                 C   J   |  |jd }t|  }| jrt|td  }|S t|d }|S )Nr   nurG   rQ   r   rR   rF   rS   r!   rT   r<   r<   r=   _print_primenu     zPrettyPrinter._print_primenuc                 C   rs  )Nr   Omegaru  rT   r<   r<   r=   _print_primeomega  rw  zPrettyPrinter._print_primeomegac                 C   s$   |j j dkr| d}|S | |S )NZdegree   °)rW   rG   rC   rT   r<   r<   r=   _print_Quantity  s   

zPrettyPrinter._print_Quantityc                 C   sD   t dt|j d }| |j}| |j}t t||| }|S )Nr   )r   r   r   rG   r   r   r   r   r   r<   r<   r=   _print_AssignmentBase  s
   z#PrettyPrinter._print_AssignmentBasec                 C   r  r?   rf  r  r<   r<   r=   
_print_Str%  rD   zPrettyPrinter._print_Strr?   )F)T)r6  r7  )NNr   F)FNr^   r_   )FNrR  Fr^   r_   )rw   
__module____qualname____doc__ZprintmethodZ_default_settingsr3   rC   propertyrF   rI   rM   rN   rV   rX   Z_print_RandomSymbolrZ   r\   rd   rj   rm   rn   rr   rt   ry   Z_print_InfinityZ_print_NegativeInfinityZ_print_EmptySetZ_print_NaturalsZ_print_Naturals0Z_print_IntegersZ_print_RationalsZ_print_ComplexesZ_print_EmptySequencerz   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r   r  r!  r5  r:  r?  rK  rM  rO  rZ  r_  rb  rc  rh  rm  rx  r|  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r   r!  r  r$  r0  r3  r5  r9  r<  r>  r?  r@  rA  rB  rC  rD  rF  rG  rH  rI  rJ  rO  rX  rZ  r[  r]  r_  rb  rc  rd  rf  rg  rh  rk  rm  rn  rq  ru  rw  rx  ry  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  Z_print_SeqPerZ_print_SeqAddZ_print_SeqMulrP   r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r#  r$  r%  r(  r)  r*  Z_print_bellr,  r-  r.  r/  r0  r2  r5  r6  r:  r>  r@  rC  rG  rI  rK  rP  rR  rT  rU  rW  r\  r_  rc  rd  re  rg  ri  rk  ro  rp  rq  rr  rv  ry  r{  r|  r}  r<   r<   r<   r=   r%      s   
					%%K6aE		

$f!# 8	0T%

		H=,			)
						r%   c                 K   s:   t |}|jd }t|}z
|| W t| S t| w )zReturns a string containing the prettified form of expr.

    For information on keyword arguments see pretty_print function.

    r+   )r%   r5   r    rI   )rB   r;   r  r+   Zuflagr<   r<   r=   r  )  s   

r  c                 K   s   t t| fi | dS )a  Prints expr in pretty form.

    pprint is just a shortcut for this function.

    Parameters
    ==========

    expr : expression
        The expression to print.

    wrap_line : bool, optional (default=True)
        Line wrapping enabled/disabled.

    num_columns : int or None, optional (default=None)
        Number of columns before line breaking (default to None which reads
        the terminal width), useful when using SymPy without terminal.

    use_unicode : bool or None, optional (default=None)
        Use unicode characters, such as the Greek letter pi instead of
        the string pi.

    full_prec : bool or string, optional (default="auto")
        Use full precision.

    order : bool or string, optional (default=None)
        Set to 'none' for long expressions if slow; default is None.

    use_unicode_sqrt_char : bool, optional (default=True)
        Use compact single-character square root symbol (when unambiguous).

    root_notation : bool, optional (default=True)
        Set to 'False' for printing exponents of the form 1/n in fractional form.
        By default exponent is printed in root form.

    mat_symbol_style : string, optional (default="plain")
        Set to "bold" for printing MatrixSymbols using a bold mathematical symbol face.
        By default the standard face is used.

    imaginary_unit : string, optional (default="i")
        Letter to use for imaginary unit when use_unicode is True.
        Can be "i" (default) or "j".
    N)printr  )rB   kwargsr<   r<   r=   pretty_print<  s   +r  c                 K   sH   ddl m} ddlm} d|vrd|d< |t| fi ||  dS )a  Prints expr using the pager, in pretty form.

    This invokes a pager command using pydoc. Lines are not wrapped
    automatically. This routine is meant to be used with a pager that allows
    sideways scrolling, like ``less -S``.

    Parameters are the same as for ``pretty_print``. If you wish to wrap lines,
    pass ``num_columns=None`` to auto-detect the width of the terminal.

    r   )pager)getpreferredencodingr,   i  N)pydocr  localer  r  encode)rB   r;   r  r  r<   r<   r=   pager_printl  s
    r  );r  Z
sympy.corer   Zsympy.core.addr   Zsympy.core.containersr   Zsympy.core.functionr   Zsympy.core.mulr   Zsympy.core.numbersr   r	   Zsympy.core.powerr
   Zsympy.core.sortingr   Zsympy.core.symbolr   Zsympy.core.sympifyr   Zsympy.printing.conventionsr   Zsympy.printing.precedencer   r   r   Zsympy.printing.printerr   r   Zsympy.printing.strr   Zsympy.utilities.iterablesr   Zsympy.utilities.exceptionsr   Z sympy.printing.pretty.stringpictr   r   Z&sympy.printing.pretty.pretty_symbologyr   r   r   r   r   r   r    r!   r"   r#   r$   Zpprint_use_unicodeZpprint_try_use_unicoder%   r  r  pprintr  r<   r<   r<   r=   <module>   sb    4                      !
-