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