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 gamma, i, x, y
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(VecSum(index_or_indices = sub_expr1, summand = ScalarMult(gamma, ScalarMult(i, TensorProd(x, y))), domain = sub_expr2), ScalarMult(gamma, TensorProd(x, VecSum(index_or_indices = sub_expr1, summand = ScalarMult(i, y), domain = sub_expr2))))

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