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, e, l
from proveit.logic import And, Iff, InSet, Union
from proveit.numbers import ModAbs, greater
from proveit.physics.quantum.QPE import _e_domain, _full_domain, _neg_domain, _pos_domain, _two_pow_t

# build up the expression from sub-expressions
sub_expr1 = greater(ModAbs(l, _two_pow_t), e)
expr = Conditional(Iff(And(InSet(l, Union(_neg_domain, _pos_domain)), sub_expr1), And(InSet(l, _full_domain), sub_expr1)).with_wrapping_at(1), InSet(e, _e_domain))

# 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\{\begin{array}{c} \begin{array}{l} \left(\left(l \in \left(\{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\} \cup \{e + 1~\ldotp \ldotp~2^{t - 1}\}\right)\right) \land \left(\left|l\right|_{\textup{mod}\thinspace 2^{t}} > e\right)\right) \\  \Leftrightarrow \left(\left(l \in \{-2^{t - 1} + 1~\ldotp \ldotp~2^{t - 1}\}\right) \land \left(\left|l\right|_{\textup{mod}\thinspace 2^{t}} > e\right)\right) \end{array} \end{array} \textrm{ if } e \in \{1~\ldotp \ldotp~2^{t - 1} - 2\}\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: 3 operands: 4
2	Operation	operator: 18 operands: 5
3	Literal
4	ExprTuple	6, 7
5	ExprTuple	50, 8
6	Operation	operator: 10 operands: 9
7	Operation	operator: 10 operands: 11
8	Operation	operator: 38 operands: 12
9	ExprTuple	13, 15
10	Literal
11	ExprTuple	14, 15
12	ExprTuple	61, 16
13	Operation	operator: 18 operands: 17
14	Operation	operator: 18 operands: 19
15	Operation	operator: 20 operands: 21
16	Operation	operator: 55 operands: 22
17	ExprTuple	35, 23
18	Literal
19	ExprTuple	35, 24
20	Literal
21	ExprTuple	50, 25
22	ExprTuple	49, 26
23	Operation	operator: 27 operands: 28
24	Operation	operator: 38 operands: 29
25	Operation	operator: 30 operands: 31
26	Operation	operator: 59 operand: 53
27	Literal
28	ExprTuple	33, 34
29	ExprTuple	41, 49
30	Literal
31	ExprTuple	35, 36
32	ExprTuple	53
33	Operation	operator: 38 operands: 37
34	Operation	operator: 38 operands: 39
35	Variable
36	Operation	operator: 51 operands: 40
37	ExprTuple	41, 42
38	Literal
39	ExprTuple	46, 49
40	ExprTuple	53, 57
41	Operation	operator: 55 operands: 43
42	Operation	operator: 59 operand: 46
43	ExprTuple	45, 61
44	ExprTuple	46
45	Operation	operator: 59 operand: 49
46	Operation	operator: 55 operands: 48
47	ExprTuple	49
48	ExprTuple	50, 61
49	Operation	operator: 51 operands: 52
50	Variable
51	Literal
52	ExprTuple	53, 54
53	Literal
54	Operation	operator: 55 operands: 56
55	Literal
56	ExprTuple	57, 58
57	Literal
58	Operation	operator: 59 operand: 61
59	Literal
60	ExprTuple	61
61	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 ¶