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, m
from proveit.logic import And, InSet
from proveit.numbers import Exp, LessEq, ModAbs, one, subtract, two
from proveit.physics.quantum.QPE import _b_floor, _m_domain, _n, _success_cond, _t, _two_pow_t

# build up the expression from sub-expressions
expr = Conditional(_success_cond, And(InSet(m, _m_domain), LessEq(ModAbs(subtract(m, _b_floor), _two_pow_t), subtract(Exp(two, subtract(_t, _n)), one))))

# 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|\frac{m}{2^{t}} - \varphi\right|_{\textup{mod}\thinspace 1} \leq 2^{-n} \textrm{ if } m \in \{0~\ldotp \ldotp~2^{t} - 1\} ,  \left|m - b_{\textit{f}}\right|_{\textup{mod}\thinspace 2^{t}} \leq \left(2^{t - n} - 1\right)\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: 23 operands: 10
7	Operation	operator: 44 operands: 11
8	Operation	operator: 12 operands: 13
9	Operation	operator: 14 operands: 15
10	ExprTuple	16, 51
11	ExprTuple	50, 54
12	Literal
13	ExprTuple	41, 17
14	Literal
15	ExprTuple	18, 19
16	Operation	operator: 48 operands: 20
17	Operation	operator: 21 operands: 22
18	Operation	operator: 23 operands: 24
19	Operation	operator: 48 operands: 25
20	ExprTuple	26, 27
21	Literal
22	ExprTuple	28, 29
23	Literal
24	ExprTuple	30, 39
25	ExprTuple	31, 40
26	Operation	operator: 32 operands: 33
27	Operation	operator: 55 operand: 38
28	Literal
29	Operation	operator: 48 operands: 35
30	Operation	operator: 48 operands: 36
31	Operation	operator: 44 operands: 37
32	Literal
33	ExprTuple	41, 39
34	ExprTuple	38
35	ExprTuple	39, 40
36	ExprTuple	41, 42
37	ExprTuple	50, 43
38	Literal
39	Operation	operator: 44 operands: 45
40	Operation	operator: 55 operand: 51
41	Variable
42	Operation	operator: 55 operand: 52
43	Operation	operator: 48 operands: 49
44	Literal
45	ExprTuple	50, 53
46	ExprTuple	51
47	ExprTuple	52
48	Literal
49	ExprTuple	53, 54
50	Literal
51	Literal
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 ¶