Expression of type Lambda ¶

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, Lambda, l
from proveit.logic import And, InSet, NotEquals
from proveit.numbers import Abs, Exp, LessEq, Mult, four, frac, one, two, zero
from proveit.physics.quantum.QPE import _diff_l_scaled_delta_floor, _full_domain, _rel_indexed_alpha

# build up the expression from sub-expressions
expr = Lambda(l, Conditional(LessEq(Exp(Abs(_rel_indexed_alpha), two), frac(one, Mult(four, Exp(_diff_l_scaled_delta_floor, 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())

l \mapsto \left\{\left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2} \leq \frac{1}{4 \cdot \left(l - \left(2^{t} \cdot \delta_{b_{\textit{f}}}\right)\right)^{2}} \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	Lambda	parameter: 44 body: 2
1	ExprTuple	44
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operands: 6
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9, 10
7	Literal
8	ExprTuple	11, 12
9	Operation	operator: 58 operands: 13
10	Operation	operator: 14 operands: 15
11	Operation	operator: 16 operands: 17
12	Operation	operator: 18 operands: 19
13	ExprTuple	20, 64
14	Literal
15	ExprTuple	67, 21
16	Literal
17	ExprTuple	44, 22
18	Literal
19	ExprTuple	44, 23
20	Operation	operator: 24 operand: 29
21	Operation	operator: 51 operands: 26
22	Operation	operator: 27 operands: 28
23	Literal
24	Literal
25	ExprTuple	29
26	ExprTuple	30, 31
27	Literal
28	ExprTuple	32, 46
29	Operation	operator: 33 operand: 37
30	Literal
31	Operation	operator: 58 operands: 35
32	Operation	operator: 53 operands: 36
33	Literal
34	ExprTuple	37
35	ExprTuple	38, 64
36	ExprTuple	39, 67
37	Operation	operator: 40 operands: 41
38	Operation	operator: 53 operands: 42
39	Operation	operator: 62 operand: 46
40	Literal
41	ExprTuple	66, 44
42	ExprTuple	44, 45
43	ExprTuple	46
44	Variable
45	Operation	operator: 62 operand: 49
46	Operation	operator: 58 operands: 48
47	ExprTuple	49
48	ExprTuple	64, 50
49	Operation	operator: 51 operands: 52
50	Operation	operator: 53 operands: 54
51	Literal
52	ExprTuple	55, 56
53	Literal
54	ExprTuple	65, 57
55	Operation	operator: 58 operands: 59
56	Operation	operator: 60 operand: 66
57	Operation	operator: 62 operand: 67
58	Literal
59	ExprTuple	64, 65
60	Literal
61	ExprTuple	66
62	Literal
63	ExprTuple	67
64	Literal
65	Literal
66	Literal
67	Literal

Expression of type Lambda¶

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

Expression of type Lambda ¶

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