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, Mult, four, three, two

# build up the expression from sub-expressions
expr = Equals(VecSum(index_or_indices = [i], summand = TensorProd(ScalarMult(beta, x), ScalarMult(beta, y)), domain = Interval(two, four)), ScalarMult(Mult(three, Exp(beta, two)), TensorProd(x, y)))

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(\left(3 \cdot \beta^{2}\right) \cdot \left(x {\otimes} y\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: 8
4	Operation	operator: 31 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameter: 28 body: 12
9	Operation	operator: 13 operands: 14
10	Operation	operator: 20 operands: 15
11	ExprTuple	28
12	Conditional	value: 16 condition: 17
13	Literal
14	ExprTuple	18, 19
15	ExprTuple	35, 37
16	Operation	operator: 20 operands: 21
17	Operation	operator: 22 operands: 23
18	Literal
19	Operation	operator: 24 operands: 25
20	Literal
21	ExprTuple	26, 27
22	Literal
23	ExprTuple	28, 29
24	Literal
25	ExprTuple	36, 38
26	Operation	operator: 31 operands: 30
27	Operation	operator: 31 operands: 32
28	Variable
29	Operation	operator: 33 operands: 34
30	ExprTuple	36, 35
31	Literal
32	ExprTuple	36, 37
33	Literal
34	ExprTuple	38, 39
35	Variable
36	Variable
37	Variable
38	Literal
39	Literal