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Expression of type Add

from the theory of proveit.physics.quantum.QPE

In [1]:
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 e, l
from proveit.numbers import Add, Exp, Interval, Sum, frac, one, subtract, two
from proveit.physics.quantum.QPE import _neg_domain, _two_pow__t_minus_one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [l]
sub_expr2 = frac(one, Exp(l, two))
expr = Add(Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = _neg_domain), Sum(index_or_indices = sub_expr1, summand = sub_expr2, domain = Interval(e, subtract(_two_pow__t_minus_one, one))))
expr:
In [3]:
# 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
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \frac{1}{l^{2}}\right) + \left(\sum_{l = e}^{2^{t - 1} - 1} \frac{1}{l^{2}}\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(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')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 44
operands: 1
1ExprTuple2, 3
2Operationoperator: 5
operand: 7
3Operationoperator: 5
operand: 8
4ExprTuple7
5Literal
6ExprTuple8
7Lambdaparameter: 29
body: 9
8Lambdaparameter: 29
body: 11
9Conditionalvalue: 13
condition: 12
10ExprTuple29
11Conditionalvalue: 13
condition: 14
12Operationoperator: 18
operands: 15
13Operationoperator: 16
operands: 17
14Operationoperator: 18
operands: 19
15ExprTuple29, 20
16Literal
17ExprTuple50, 21
18Literal
19ExprTuple29, 22
20Operationoperator: 25
operands: 23
21Operationoperator: 40
operands: 24
22Operationoperator: 25
operands: 26
23ExprTuple27, 28
24ExprTuple29, 42
25Literal
26ExprTuple39, 30
27Operationoperator: 44
operands: 31
28Operationoperator: 48
operand: 35
29Variable
30Operationoperator: 44
operands: 33
31ExprTuple34, 50
32ExprTuple35
33ExprTuple38, 47
34Operationoperator: 48
operand: 38
35Operationoperator: 44
operands: 37
36ExprTuple38
37ExprTuple39, 50
38Operationoperator: 40
operands: 41
39Variable
40Literal
41ExprTuple42, 43
42Literal
43Operationoperator: 44
operands: 45
44Literal
45ExprTuple46, 47
46Literal
47Operationoperator: 48
operand: 50
48Literal
49ExprTuple50
50Literal