Expression of type ExprTuple

from the theory of proveit.linear_algebra.tensors

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, Function, s
from proveit.core_expr_types import Q__b_1_to_j, a_1_to_i, b_1_to_j, c_1_to_k, f__b_1_to_j
from proveit.linear_algebra import ScalarMult, TensorProd, VecSum

# build up the expression from sub-expressions
sub_expr1 = [b_1_to_j]
sub_expr2 = Function(s, sub_expr1)
expr = ExprTuple(TensorProd(a_1_to_i, VecSum(index_or_indices = sub_expr1, summand = ScalarMult(sub_expr2, f__b_1_to_j), condition = Q__b_1_to_j), c_1_to_k), VecSum(index_or_indices = sub_expr1, summand = ScalarMult(sub_expr2, TensorProd(a_1_to_i, f__b_1_to_j, c_1_to_k)), condition = Q__b_1_to_j))

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(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} \left[\sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(s\left(b_{1}, b_{2}, \ldots, b_{j}\right) \cdot f\left(b_{1}, b_{2}, \ldots, b_{j}\right)\right)\right]{\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}, \sum_{b_{1}, b_{2}, \ldots, b_{j}~|~Q\left(b_{1}, b_{2}, \ldots, b_{j}\right)}~\left(s\left(b_{1}, b_{2}, \ldots, b_{j}\right) \cdot \left(a_{1} {\otimes}  a_{2} {\otimes}  \ldots {\otimes}  a_{i} {\otimes} f\left(b_{1}, b_{2}, \ldots, b_{j}\right){\otimes} c_{1} {\otimes}  c_{2} {\otimes}  \ldots {\otimes}  c_{k}\right)\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: 20 operands: 3
2	Operation	operator: 7 operand: 6
3	ExprTuple	23, 5, 25
4	ExprTuple	6
5	Operation	operator: 7 operand: 10
6	Lambda	parameters: 30 body: 9
7	Literal
8	ExprTuple	10
9	Conditional	value: 11 condition: 15
10	Lambda	parameters: 30 body: 12
11	Operation	operator: 17 operands: 13
12	Conditional	value: 14 condition: 15
13	ExprTuple	22, 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 30
16	Operation	operator: 20 operands: 21
17	Literal
18	ExprTuple	22, 24
19	Variable
20	Literal
21	ExprTuple	23, 24, 25
22	Operation	operator: 26 operands: 30
23	ExprRange	lambda_map: 27 start_index: 38 end_index: 28
24	Operation	operator: 29 operands: 30
25	ExprRange	lambda_map: 31 start_index: 38 end_index: 32
26	Variable
27	Lambda	parameter: 44 body: 33
28	Variable
29	Variable
30	ExprTuple	34
31	Lambda	parameter: 44 body: 35
32	Variable
33	IndexedVar	variable: 36 index: 44
34	ExprRange	lambda_map: 37 start_index: 38 end_index: 39
35	IndexedVar	variable: 40 index: 44
36	Variable
37	Lambda	parameter: 44 body: 41
38	Literal
39	Variable
40	Variable
41	IndexedVar	variable: 42 index: 44
42	Variable
43	ExprTuple	44
44	Variable