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, gamma, i, x, y
from proveit.linear_algebra import ScalarMult, TensorProd, VecSum
from proveit.logic import Equals
from proveit.numbers import Add, Interval, Mult, four, one, two

# build up the expression from sub-expressions
sub_expr1 = [i]
sub_expr2 = Mult(gamma, beta)
sub_expr3 = Add(i, one)
sub_expr4 = TensorProd(x, y)
sub_expr5 = Interval(two, four)
expr = Equals(VecSum(index_or_indices = sub_expr1, summand = ScalarMult(Mult(sub_expr2, i, sub_expr3), sub_expr4), domain = sub_expr5), VecSum(index_or_indices = sub_expr1, summand = ScalarMult(Mult(sub_expr2, Mult(i, sub_expr3)), sub_expr4), domain = sub_expr5))

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(\left(\gamma \cdot \beta\right) \cdot i \cdot \left(i + 1\right)\right) \cdot \left(x {\otimes} y\right)\right)\right) = \left(\sum_{i=2}^{4} \left(\left(\left(\gamma \cdot \beta\right) \cdot \left(i \cdot \left(i + 1\right)\right)\right) \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: 45 body: 10
9	Lambda	parameter: 45 body: 12
10	Conditional	value: 13 condition: 15
11	ExprTuple	45
12	Conditional	value: 14 condition: 15
13	Operation	operator: 17 operands: 16
14	Operation	operator: 17 operands: 18
15	Operation	operator: 19 operands: 20
16	ExprTuple	21, 23
17	Literal
18	ExprTuple	22, 23
19	Literal
20	ExprTuple	45, 24
21	Operation	operator: 38 operands: 25
22	Operation	operator: 38 operands: 26
23	Operation	operator: 27 operands: 28
24	Operation	operator: 29 operands: 30
25	ExprTuple	31, 45, 42
26	ExprTuple	31, 32
27	Literal
28	ExprTuple	33, 34
29	Literal
30	ExprTuple	35, 36
31	Operation	operator: 38 operands: 37
32	Operation	operator: 38 operands: 39
33	Variable
34	Variable
35	Literal
36	Literal
37	ExprTuple	40, 41
38	Literal
39	ExprTuple	45, 42
40	Variable
41	Variable
42	Operation	operator: 43 operands: 44
43	Literal
44	ExprTuple	45, 46
45	Variable
46	Literal