Expression of type Mult

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
from proveit.trigonometry import Sin

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

expr:

# 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())

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

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	()	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

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