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
from proveit.logic import Equals
from proveit.numbers import Add, Mult, one

# build up the expression from sub-expressions
sub_expr1 = Add(i, one)
sub_expr2 = TensorProd(x, y)
expr = Equals(ScalarMult(ScalarMult(gamma, i), ScalarMult(beta, ScalarMult(sub_expr1, sub_expr2))), ScalarMult(Mult(gamma, i, beta, sub_expr1), sub_expr2))

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(\gamma \cdot i\right) \cdot \left(\beta \cdot \left(\left(i + 1\right) \cdot \left(x {\otimes} y\right)\right)\right)\right) = \left(\left(\gamma \cdot i \cdot \beta \cdot \left(i + 1\right)\right) \cdot \left(x {\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: 17 operands: 5
4	Operation	operator: 17 operands: 6
5	ExprTuple	7, 8
6	ExprTuple	9, 20
7	Operation	operator: 17 operands: 10
8	Operation	operator: 17 operands: 11
9	Operation	operator: 12 operands: 13
10	ExprTuple	15, 25
11	ExprTuple	16, 14
12	Literal
13	ExprTuple	15, 25, 16, 19
14	Operation	operator: 17 operands: 18
15	Variable
16	Variable
17	Literal
18	ExprTuple	19, 20
19	Operation	operator: 21 operands: 22
20	Operation	operator: 23 operands: 24
21	Literal
22	ExprTuple	25, 26
23	Literal
24	ExprTuple	27, 28
25	Variable
26	Literal
27	Variable
28	Variable