Expression of type Conditional ¶

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 Conditional, l
from proveit.logic import And, InSet, NotEquals
from proveit.numbers import Abs, IntervalOC, Mult, frac, pi, subtract, two, zero
from proveit.physics.quantum.QPE import _delta_b_floor, _full_domain, _two_pow_t

# build up the expression from sub-expressions
expr = Conditional(InSet(Mult(pi, Abs(subtract(_delta_b_floor, frac(l, _two_pow_t)))), IntervalOC(zero, frac(pi, two))), And(InSet(l, _full_domain), NotEquals(l, zero)))

# 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(\pi \cdot \left|\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right|\right) \in \left(0,\frac{\pi}{2}\right] \textrm{ if } l \in \{-2^{t - 1} + 1~\ldotp \ldotp~2^{t - 1}\} ,  l \neq 0\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Conditional	value: 1 condition: 2
1	Operation	operator: 14 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7
4	Literal
5	ExprTuple	8, 9
6	Operation	operator: 10 operands: 11
7	Operation	operator: 12 operands: 13
8	Operation	operator: 14 operands: 15
9	Operation	operator: 16 operands: 17
10	Literal
11	ExprTuple	28, 18
12	Literal
13	ExprTuple	21, 19
14	Literal
15	ExprTuple	45, 20
16	Literal
17	ExprTuple	45, 21
18	Operation	operator: 22 operand: 27
19	Operation	operator: 42 operands: 24
20	Operation	operator: 25 operands: 26
21	Literal
22	Literal
23	ExprTuple	27
24	ExprTuple	28, 52
25	Literal
26	ExprTuple	29, 41
27	Operation	operator: 50 operands: 30
28	Literal
29	Operation	operator: 50 operands: 31
30	ExprTuple	32, 33
31	ExprTuple	34, 57
32	Operation	operator: 35 operand: 39
33	Operation	operator: 55 operand: 40
34	Operation	operator: 55 operand: 41
35	Literal
36	ExprTuple	39
37	ExprTuple	40
38	ExprTuple	41
39	Literal
40	Operation	operator: 42 operands: 43
41	Operation	operator: 48 operands: 44
42	Literal
43	ExprTuple	45, 46
44	ExprTuple	52, 47
45	Variable
46	Operation	operator: 48 operands: 49
47	Operation	operator: 50 operands: 51
48	Literal
49	ExprTuple	52, 53
50	Literal
51	ExprTuple	53, 54
52	Literal
53	Literal
54	Operation	operator: 55 operand: 57
55	Literal
56	ExprTuple	57
57	Literal

Expression of type Conditional¶

from the theory of proveit.physics.quantum.QPE¶

Expression of type Conditional ¶

from the theory of proveit.physics.quantum.QPE ¶