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 = Exp(_eps, two)
sub_expr2 = frac(one, _eps)
sub_expr3 = Add(three, sub_expr2)
sub_expr4 = Mult(sub_expr1, Exp(Add(two, sub_expr2), two))
expr = Equals(frac(Mult(sub_expr1, sub_expr3), sub_expr4), frac(Mult(_eps, Mult(Exp(_eps, subtract(two, one)), sub_expr3)), 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())

\frac{\epsilon^{2} \cdot \left(3 + \frac{1}{\epsilon}\right)}{\epsilon^{2} \cdot \left(2 + \frac{1}{\epsilon}\right)^{2}} = \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: 32 operands: 5
4	Operation	operator: 32 operands: 6
5	ExprTuple	7, 9
6	ExprTuple	8, 9
7	Operation	operator: 16 operands: 10
8	Operation	operator: 16 operands: 11
9	Operation	operator: 16 operands: 12
10	ExprTuple	14, 21
11	ExprTuple	36, 13
12	ExprTuple	14, 15
13	Operation	operator: 16 operands: 17
14	Operation	operator: 23 operands: 18
15	Operation	operator: 23 operands: 19
16	Literal
17	ExprTuple	20, 21
18	ExprTuple	36, 34
19	ExprTuple	22, 34
20	Operation	operator: 23 operands: 24
21	Operation	operator: 30 operands: 25
22	Operation	operator: 30 operands: 26
23	Literal
24	ExprTuple	36, 27
25	ExprTuple	28, 29
26	ExprTuple	34, 29
27	Operation	operator: 30 operands: 31
28	Literal
29	Operation	operator: 32 operands: 33
30	Literal
31	ExprTuple	34, 35
32	Literal
33	ExprTuple	39, 36
34	Literal
35	Operation	operator: 37 operand: 39
36	Literal
37	Literal
38	ExprTuple	39
39	Literal