Expression of type Abs ¶

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 l
from proveit.numbers import Abs, Exp, Mult, e, frac, i, one, pi, subtract, two
from proveit.physics.quantum.QPE import _delta_b_floor, _two_pow_t

# build up the expression from sub-expressions
expr = Abs(Mult(frac(one, _two_pow_t), frac(subtract(one, Exp(e, Mult(two, pi, i, subtract(Mult(_two_pow_t, _delta_b_floor), l)))), subtract(one, Exp(e, Mult(two, pi, i, subtract(_delta_b_floor, frac(l, _two_pow_t))))))))

# 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|\frac{1}{2^{t}} \cdot \frac{1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\left(2^{t} \cdot \delta_{b_{\textit{f}}}\right) - l\right)}}{1 - \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \left(\delta_{b_{\textit{f}}} - \frac{l}{2^{t}}\right)}}\right|

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

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

Expression of type Abs¶

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

Expression of type Abs ¶

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