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 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 = 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)))))))

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{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)}}

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