Expression of type ExprTuple

from the theory of proveit.physics.quantum.circuits

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import ExprTuple
from proveit.core_expr_types.expr_arrays import A11_to_Akl_varray, B11_to_Bkl_varray
from proveit.logic import Equals
from proveit.physics.quantum.circuits import circuit_Akl, circuit_Bkl

# build up the expression from sub-expressions
expr = ExprTuple(Equals(A11_to_Akl_varray, B11_to_Bkl_varray), Equals(circuit_Akl, circuit_Bkl))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\left(\begin{array}{cccc} 
 A_{1, 1} & A_{2, 1} & \cdots & A_{k, 1} \\
A_{1, 2} & A_{2, 2} & \cdots & A_{k, 2} \\
\vdots & \vdots & \ddots & \vdots \\
A_{1, l} & A_{2, l} & \cdots & A_{k, l} \\
\end{array}
\right) = \left(\begin{array}{cccc} 
 B_{1, 1} & B_{2, 1} & \cdots & B_{k, 1} \\
B_{1, 2} & B_{2, 2} & \cdots & B_{k, 2} \\
\vdots & \vdots & \ddots & \vdots \\
B_{1, l} & B_{2, l} & \cdots & B_{k, l} \\
\end{array}
\right), \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \gate{A_{1, 1}} \qwx[1] & \gate{A_{2, 1}} \qwx[1] & \gate{\cdots} \qwx[1] & \gate{A_{k, 1}} \qwx[1] & \qw \\
& \gate{A_{1, 2}} \qwx[1] & \gate{A_{2, 2}} \qwx[1] & \gate{\cdots} \qwx[1] & \gate{A_{k, 2}} \qwx[1] & \qw \\
& \gate{\vdots} \qwx[1] & \gate{\vdots} \qwx[1] & \gate{\ddots} \qwx[1] & \gate{\vdots} \qwx[1] & \qw \\
& \gate{A_{1, l}} & \gate{A_{2, l}} & \gate{\cdots} & \gate{A_{k, l}} & \qw
} \end{array}\right) = \left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
& \gate{B_{1, 1}} \qwx[1] & \gate{B_{2, 1}} \qwx[1] & \gate{\cdots} \qwx[1] & \gate{B_{k, 1}} \qwx[1] & \qw \\
& \gate{B_{1, 2}} \qwx[1] & \gate{B_{2, 2}} \qwx[1] & \gate{\cdots} \qwx[1] & \gate{B_{k, 2}} \qwx[1] & \qw \\
& \gate{\vdots} \qwx[1] & \gate{\vdots} \qwx[1] & \gate{\ddots} \qwx[1] & \gate{\vdots} \qwx[1] & \qw \\
& \gate{B_{1, l}} & \gate{B_{2, l}} & \gate{\cdots} & \gate{B_{k, l}} & \qw
} \end{array}\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	8, 10
4	Literal
5	ExprTuple	6, 7
6	Operation	operator: 9 operands: 8
7	Operation	operator: 9 operands: 10
8	ExprTuple	11
9	Literal
10	ExprTuple	12
11	ExprRange	lambda_map: 13 start_index: 23 end_index: 15
12	ExprRange	lambda_map: 14 start_index: 23 end_index: 15
13	Lambda	parameter: 31 body: 16
14	Lambda	parameter: 31 body: 18
15	Variable
16	ExprTuple	19
17	ExprTuple	31
18	ExprTuple	20
19	ExprRange	lambda_map: 21 start_index: 23 end_index: 24
20	ExprRange	lambda_map: 22 start_index: 23 end_index: 24
21	Lambda	parameter: 32 body: 25
22	Lambda	parameter: 32 body: 27
23	Literal
24	Variable
25	IndexedVar	variable: 28 indices: 30
26	ExprTuple	32
27	IndexedVar	variable: 29 indices: 30
28	Variable
29	Variable
30	ExprTuple	31, 32
31	Variable
32	Variable