Expression of type ExprTuple

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 ExprTuple, Variable, t
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.numbers import Add, Exp, Mult, e, frac, i, one, pi, subtract, two
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase, two_pow_t

# build up the expression from sub-expressions
expr = ExprTuple(ScalarMult(frac(one, Exp(two, subtract(frac(Add(t, one), two), frac(t, two)))), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, _phase, two_pow_t)), ket1))), Variable("_a", latex_format = r"{_{-}a}"))

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())

\left(\frac{1}{2^{\frac{t + 1}{2} - \frac{t}{2}}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot 2^{t}} \cdot \lvert 1 \rangle\right)\right), {_{-}a}\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

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