Expression of type Equals

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 A, ExprRange, Function, IndexedVar, Variable, n, v
from proveit.core_expr_types import A_1_to_n, v_1_to_n
from proveit.linear_algebra import TensorProd
from proveit.logic import Equals
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals(Function(TensorProd(A_1_to_n), [TensorProd(v_1_to_n)]), TensorProd(ExprRange(sub_expr1, Function(IndexedVar(A, sub_expr1), [IndexedVar(v, sub_expr1)]), one, n)))

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_{n}\right)\left(v_{1} {\otimes}  v_{2} {\otimes}  \ldots {\otimes}  v_{n}\right) = \left(A_{1}\left(v_{1}\right) {\otimes}  A_{2}\left(v_{2}\right) {\otimes}  \ldots {\otimes}  A_{n}\left(v_{n}\right)\right)

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',)
direction	Direction of the relation (normal or reversed)	normal	normal	('with_direction_reversed', 'is_reversed')

# 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
3	Operation	operator: 5 operand: 9
4	Operation	operator: 12 operands: 7
5	Operation	operator: 12 operands: 8
6	ExprTuple	9
7	ExprTuple	10
8	ExprTuple	11
9	Operation	operator: 12 operands: 13
10	ExprRange	lambda_map: 14 start_index: 19 end_index: 20
11	ExprRange	lambda_map: 15 start_index: 19 end_index: 20
12	Literal
13	ExprTuple	16
14	Lambda	parameter: 27 body: 17
15	Lambda	parameter: 27 body: 21
16	ExprRange	lambda_map: 18 start_index: 19 end_index: 20
17	Operation	operator: 21 operand: 24
18	Lambda	parameter: 27 body: 24
19	Literal
20	Variable
21	IndexedVar	variable: 23 index: 27
22	ExprTuple	24
23	Variable
24	IndexedVar	variable: 25 index: 27
25	Variable
26	ExprTuple	27
27	Variable