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
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 TensorProd, VecSum
from proveit.linear_algebra.addition import vec_summation_b1toj_fQ

# build up the expression from sub-expressions
expr = ExprTuple(VecSum(index_or_indices = [b_1_to_j], summand = TensorProd(a_1_to_i, f__b_1_to_j, c_1_to_k), condition = Q__b_1_to_j), TensorProd(a_1_to_i, vec_summation_b1toj_fQ, c_1_to_k))

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