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 = Add(i, one)
sub_expr3 = TensorProd(x, y)
sub_expr4 = Interval(two, four)
expr = Equals(VecSum(index_or_indices = sub_expr1, summand = ScalarMult(Mult(gamma, i, beta, sub_expr2), sub_expr3), domain = sub_expr4), ScalarMult(Mult(gamma, beta), VecSum(index_or_indices = sub_expr1, summand = ScalarMult(Mult(i, sub_expr2), sub_expr3), domain = sub_expr4)))

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(\gamma \cdot i \cdot \beta \cdot \left(i + 1\right)\right) \cdot \left(x {\otimes} y\right)\right)\right) = \left(\left(\gamma \cdot \beta\right) \cdot \left(\sum_{i=2}^{4} \left(\left(i \cdot \left(i + 1\right)\right) \cdot \left(x {\otimes} 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: 12 operand: 7
4	Operation	operator: 23 operands: 6
5	ExprTuple	7
6	ExprTuple	8, 9
7	Lambda	parameter: 45 body: 10
8	Operation	operator: 32 operands: 11
9	Operation	operator: 12 operand: 15
10	Conditional	value: 14 condition: 21
11	ExprTuple	27, 28
12	Literal
13	ExprTuple	15
14	Operation	operator: 23 operands: 16
15	Lambda	parameter: 45 body: 18
16	ExprTuple	19, 30
17	ExprTuple	45
18	Conditional	value: 20 condition: 21
19	Operation	operator: 32 operands: 22
20	Operation	operator: 23 operands: 24
21	Operation	operator: 25 operands: 26
22	ExprTuple	27, 45, 28, 38
23	Literal
24	ExprTuple	29, 30
25	Literal
26	ExprTuple	45, 31
27	Variable
28	Variable
29	Operation	operator: 32 operands: 33
30	Operation	operator: 34 operands: 35
31	Operation	operator: 36 operands: 37
32	Literal
33	ExprTuple	45, 38
34	Literal
35	ExprTuple	39, 40
36	Literal
37	ExprTuple	41, 42
38	Operation	operator: 43 operands: 44
39	Variable
40	Variable
41	Literal
42	Literal
43	Literal
44	ExprTuple	45, 46
45	Variable
46	Literal