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(ScalarMult(gamma, i), ScalarMult(beta, ScalarMult(sub_expr2, sub_expr3))), domain = sub_expr4), VecSum(index_or_indices = sub_expr1, summand = ScalarMult(Mult(gamma, i, beta, 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\right) \cdot \left(\beta \cdot \left(\left(i + 1\right) \cdot \left(x {\otimes} y\right)\right)\right)\right)\right) = \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)

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: 43 body: 10
9	Lambda	parameter: 43 body: 12
10	Conditional	value: 13 condition: 15
11	ExprTuple	43
12	Conditional	value: 14 condition: 15
13	Operation	operator: 35 operands: 16
14	Operation	operator: 35 operands: 17
15	Operation	operator: 18 operands: 19
16	ExprTuple	20, 21
17	ExprTuple	22, 38
18	Literal
19	ExprTuple	43, 23
20	Operation	operator: 35 operands: 24
21	Operation	operator: 35 operands: 25
22	Operation	operator: 26 operands: 27
23	Operation	operator: 28 operands: 29
24	ExprTuple	31, 43
25	ExprTuple	32, 30
26	Literal
27	ExprTuple	31, 43, 32, 37
28	Literal
29	ExprTuple	33, 34
30	Operation	operator: 35 operands: 36
31	Variable
32	Variable
33	Literal
34	Literal
35	Literal
36	ExprTuple	37, 38
37	Operation	operator: 39 operands: 40
38	Operation	operator: 41 operands: 42
39	Literal
40	ExprTuple	43, 44
41	Literal
42	ExprTuple	45, 46
43	Variable
44	Literal
45	Variable
46	Variable