Expression of type ExprRange

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 ExprRange, Variable, t
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.logic import CartExp, InSet
from proveit.numbers import Add, Complex, Exp, Mult, Neg, e, frac, i, one, pi, sqrt, two, zero
from proveit.physics.quantum import ket0, ket1
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprRange(sub_expr1, InSet(ScalarMult(frac(one, sqrt(two)), VecAdd(ket0, ScalarMult(Exp(e, Mult(two, pi, i, Exp(two, Neg(sub_expr1)), _phase)), ket1))), CartExp(Complex, Exp(two, one))), Add(Neg(t), two), zero)

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(\left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-\left(-t + 2\right)} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right) \in \mathbb{C}^{2^{1}}\right), \left(\left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-\left(-t + 3\right)} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right) \in \mathbb{C}^{2^{1}}\right), \ldots, \left(\left(\frac{1}{\sqrt{2}} \cdot \left(\lvert 0 \rangle + \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot 2^{-0} \cdot \varphi} \cdot \lvert 1 \rangle\right)\right)\right) \in \mathbb{C}^{2^{1}}\right)

stored_expr.style_options()

name	description	default	current value	related methods
parameterization	'implicit' (default for LaTeX formatting) hides the parameter the ExprRange so the parameterization may be ambiguous (e.g., x_{1+1}, ..., x_{n+1}); 'explicit' (default for string formatting) reveals the parameterization (e.g. x_{1+1}, ..x_{k+1}.., x_{n+1}).	None	None/False	('with_explicit_parameterization', 'with_implicit_parameterization', 'with_default_parameterization_style')
front_expansion	The number of instances to display at the front of the range (e.g., before the ellipsis). Default is 2.	2	2	('with_front_expansion', 'get_front_expansion')
back_expansion	The number of instances to display at the back of the range (e.g., after the ellipsis). Default is 1.	1	1	('with_back_expansion', 'get_back_expansion')
order	The default order is 'increasing' (a_1 ... a_3) but to represent a 'decreasing' ExprRange (a_6 ... a_2) the order must be set to 'decreasing'	increasing	increasing	('with_decreasing_order', 'with_increasing_order')
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
case_simplify	If 'True', simplify formatted instances that are ConditionalSets under proper index assumptions	False	False	('with_case_simplification',)

# display the expression information
stored_expr.expr_info()

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