Expression of type Equals

from the theory of proveit.physics.quantum.QPE

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.logic import Equals
from proveit.numbers import Add, Exp, Mult, frac, one, subtract, three, two
from proveit.physics.quantum.QPE import _eps

# build up the expression from sub-expressions
sub_expr1 = frac(one, _eps)
sub_expr2 = Mult(Exp(_eps, subtract(two, one)), Add(three, sub_expr1))
sub_expr3 = Mult(Exp(_eps, two), Exp(Add(two, sub_expr1), two))
expr = Equals(Mult(_eps, frac(sub_expr2, sub_expr3)), frac(Mult(_eps, sub_expr2), 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(\epsilon \cdot \frac{\epsilon^{2 - 1} \cdot \left(3 + \frac{1}{\epsilon}\right)}{\epsilon^{2} \cdot \left(2 + \frac{1}{\epsilon}\right)^{2}}\right) = \frac{\epsilon \cdot \left(\epsilon^{2 - 1} \cdot \left(3 + \frac{1}{\epsilon}\right)\right)}{\epsilon^{2} \cdot \left(2 + \frac{1}{\epsilon}\right)^{2}}

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: 14 operands: 5
4	Operation	operator: 34 operands: 6
5	ExprTuple	38, 7
6	ExprTuple	8, 11
7	Operation	operator: 34 operands: 9
8	Operation	operator: 14 operands: 10
9	ExprTuple	12, 11
10	ExprTuple	38, 12
11	Operation	operator: 14 operands: 13
12	Operation	operator: 14 operands: 15
13	ExprTuple	16, 17
14	Literal
15	ExprTuple	18, 19
16	Operation	operator: 22 operands: 20
17	Operation	operator: 22 operands: 21
18	Operation	operator: 22 operands: 23
19	Operation	operator: 29 operands: 24
20	ExprTuple	38, 32
21	ExprTuple	25, 32
22	Literal
23	ExprTuple	38, 26
24	ExprTuple	27, 31
25	Operation	operator: 29 operands: 28
26	Operation	operator: 29 operands: 30
27	Literal
28	ExprTuple	32, 31
29	Literal
30	ExprTuple	32, 33
31	Operation	operator: 34 operands: 35
32	Literal
33	Operation	operator: 36 operand: 39
34	Literal
35	ExprTuple	39, 38
36	Literal
37	ExprTuple	39
38	Literal
39	Literal