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

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(\gamma \cdot \left(i \cdot \left(\beta \cdot \left(\left(i + 1\right) \cdot \left(x {\otimes} y\right)\right)\right)\right)\right)\right) = \left(\left(\gamma \cdot \beta\right) \cdot \left(x {\otimes} \left(\sum_{i=2}^{4} \left(\left(i \cdot \left(i + 1\right)\right) \cdot 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: 16 operand: 7
4	Operation	operator: 35 operands: 6
5	ExprTuple	7
6	ExprTuple	8, 9
7	Lambda	parameter: 51 body: 10
8	Operation	operator: 37 operands: 11
9	Operation	operator: 45 operands: 12
10	Conditional	value: 13 condition: 26
11	ExprTuple	18, 31
12	ExprTuple	49, 14
13	Operation	operator: 35 operands: 15
14	Operation	operator: 16 operand: 20
15	ExprTuple	18, 19
16	Literal
17	ExprTuple	20
18	Variable
19	Operation	operator: 35 operands: 21
20	Lambda	parameter: 51 body: 23
21	ExprTuple	51, 24
22	ExprTuple	51
23	Conditional	value: 25 condition: 26
24	Operation	operator: 35 operands: 27
25	Operation	operator: 35 operands: 28
26	Operation	operator: 29 operands: 30
27	ExprTuple	31, 32
28	ExprTuple	33, 50
29	Literal
30	ExprTuple	51, 34
31	Variable
32	Operation	operator: 35 operands: 36
33	Operation	operator: 37 operands: 38
34	Operation	operator: 39 operands: 40
35	Literal
36	ExprTuple	42, 41
37	Literal
38	ExprTuple	51, 42
39	Literal
40	ExprTuple	43, 44
41	Operation	operator: 45 operands: 46
42	Operation	operator: 47 operands: 48
43	Literal
44	Literal
45	Literal
46	ExprTuple	49, 50
47	Literal
48	ExprTuple	51, 52
49	Variable
50	Variable
51	Variable
52	Literal