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