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 fi, gamma, i, x, y, z
from proveit.linear_algebra import ScalarMult, TensorProd, VecSum
from proveit.logic import Equals
from proveit.numbers import Interval, four, two

# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = Interval(two, four)
sub_expr3 = TensorProd(y, fi)
expr = Equals(VecSum(index_or_indices = sub_expr1, summand = ScalarMult(gamma, TensorProd(x, sub_expr3, z)), domain = sub_expr2), TensorProd(x, VecSum(index_or_indices = sub_expr1, summand = ScalarMult(gamma, sub_expr3), domain = sub_expr2), z))

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_{i=2}^{4} \left(\gamma \cdot \left(x {\otimes} \left(y {\otimes} f\left(i\right)\right) {\otimes} z\right)\right)\right) = \left(x {\otimes} \left(\sum_{i=2}^{4} \left(\gamma \cdot \left(y {\otimes} f\left(i\right)\right)\right)\right) {\otimes} z\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: 10 operand: 7
4	Operation	operator: 29 operands: 6
5	ExprTuple	7
6	ExprTuple	24, 8, 25
7	Lambda	parameter: 39 body: 9
8	Operation	operator: 10 operand: 13
9	Conditional	value: 12 condition: 18
10	Literal
11	ExprTuple	13
12	Operation	operator: 20 operands: 14
13	Lambda	parameter: 39 body: 15
14	ExprTuple	26, 16
15	Conditional	value: 17 condition: 18
16	Operation	operator: 29 operands: 19
17	Operation	operator: 20 operands: 21
18	Operation	operator: 22 operands: 23
19	ExprTuple	24, 27, 25
20	Literal
21	ExprTuple	26, 27
22	Literal
23	ExprTuple	39, 28
24	Variable
25	Variable
26	Variable
27	Operation	operator: 29 operands: 30
28	Operation	operator: 31 operands: 32
29	Literal
30	ExprTuple	33, 34
31	Literal
32	ExprTuple	35, 36
33	Variable
34	Operation	operator: 37 operand: 39
35	Literal
36	Literal
37	Variable
38	ExprTuple	39
39	Variable