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 import ExprRange, Variable, m
from proveit.core_expr_types import Len
from proveit.logic import Equals
from proveit.numbers import Floor, ModAbs, Mult, Neg, one, subtract, two
from proveit.physics.quantum.QPE import _phase, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = Mult(_two_pow_t, _phase)
expr = Equals(Len(operands = [ModAbs(subtract(m, sub_expr2), _two_pow_t), Neg(ModAbs(subtract(m, Floor(sub_expr2)), _two_pow_t))]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, two)]))

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|m - \left(2^{t} \cdot \varphi\right)\right|_{\textup{mod}\thinspace 2^{t}}, -\left|m - \left\lfloor 2^{t} \cdot \varphi\right\rfloor\right|_{\textup{mod}\thinspace 2^{t}}\right)| = |\left(1, \ldots, 2\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 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	8, 9
6	Literal
7	ExprTuple	10
8	Operation	operator: 19 operands: 11
9	Operation	operator: 28 operand: 16
10	ExprRange	lambda_map: 13 start_index: 14 end_index: 40
11	ExprTuple	15, 36
12	ExprTuple	16
13	Lambda	parameter: 21 body: 21
14	Literal
15	Operation	operator: 24 operands: 18
16	Operation	operator: 19 operands: 20
17	ExprTuple	21
18	ExprTuple	26, 22
19	Literal
20	ExprTuple	23, 36
21	Variable
22	Operation	operator: 28 operand: 33
23	Operation	operator: 24 operands: 25
24	Literal
25	ExprTuple	26, 27
26	Variable
27	Operation	operator: 28 operand: 30
28	Literal
29	ExprTuple	30
30	Operation	operator: 31 operand: 33
31	Literal
32	ExprTuple	33
33	Operation	operator: 34 operands: 35
34	Literal
35	ExprTuple	36, 37
36	Operation	operator: 38 operands: 39
37	Literal
38	Literal
39	ExprTuple	40, 41
40	Literal
41	Literal