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)
expr = Equals(TensorProd(x, VecSum(index_or_indices = sub_expr1, summand = ScalarMult(gamma, TensorProd(y, fi)), domain = sub_expr2), z), ScalarMult(gamma, TensorProd(x, y, VecSum(index_or_indices = sub_expr1, summand = fi, 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(x {\otimes} \left(\sum_{i=2}^{4} \left(\gamma \cdot \left(y {\otimes} f\left(i\right)\right)\right)\right) {\otimes} z\right) = \left(\gamma \cdot \left(x {\otimes} y {\otimes} \left(\sum_{i=2}^{4} f\left(i\right)\right) {\otimes} z\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: 26 operands: 5
4	Operation	operator: 20 operands: 6
5	ExprTuple	12, 7, 14
6	ExprTuple	23, 8
7	Operation	operator: 16 operand: 11
8	Operation	operator: 26 operands: 10
9	ExprTuple	11
10	ExprTuple	12, 30, 13, 14
11	Lambda	parameter: 37 body: 15
12	Variable
13	Operation	operator: 16 operand: 19
14	Variable
15	Conditional	value: 18 condition: 25
16	Literal
17	ExprTuple	19
18	Operation	operator: 20 operands: 21
19	Lambda	parameter: 37 body: 22
20	Literal
21	ExprTuple	23, 24
22	Conditional	value: 31 condition: 25
23	Variable
24	Operation	operator: 26 operands: 27
25	Operation	operator: 28 operands: 29
26	Literal
27	ExprTuple	30, 31
28	Literal
29	ExprTuple	37, 32
30	Variable
31	Operation	operator: 33 operand: 37
32	Operation	operator: 35 operands: 36
33	Variable
34	ExprTuple	37
35	Literal
36	ExprTuple	38, 39
37	Variable
38	Literal
39	Literal