Expression of type TensorProd

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 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]
expr = TensorProd(a_1_to_i, VecSum(index_or_indices = sub_expr1, summand = ScalarMult(Function(s, sub_expr1), f__b_1_to_j), condition = Q__b_1_to_j), 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())

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}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 1 operands: 2
1	Literal
2	ExprTuple	3, 4, 5
3	ExprRange	lambda_map: 6 start_index: 30 end_index: 7
4	Operation	operator: 8 operand: 13
5	ExprRange	lambda_map: 10 start_index: 30 end_index: 11
6	Lambda	parameter: 35 body: 12
7	Variable
8	Literal
9	ExprTuple	13
10	Lambda	parameter: 35 body: 14
11	Variable
12	IndexedVar	variable: 15 index: 35
13	Lambda	parameters: 27 body: 16
14	IndexedVar	variable: 17 index: 35
15	Variable
16	Conditional	value: 18 condition: 19
17	Variable
18	Operation	operator: 20 operands: 21
19	Operation	operator: 22 operands: 27
20	Literal
21	ExprTuple	23, 24
22	Variable
23	Operation	operator: 25 operands: 27
24	Operation	operator: 26 operands: 27
25	Variable
26	Variable
27	ExprTuple	28
28	ExprRange	lambda_map: 29 start_index: 30 end_index: 31
29	Lambda	parameter: 35 body: 32
30	Literal
31	Variable
32	IndexedVar	variable: 33 index: 35
33	Variable
34	ExprTuple	35
35	Variable